Question 1 :
The length of the diameter of the circle ${x^2} + {y^2} - 4x - 6y + 4 = 0$
Question 5 :
If the lines $3x - 4y - 7 = 0$ and $2s - 3y - 5 = 0$ are two diameters of a circle of area $49\pi$ square units, the equation of the circle is-
Question 6 :
The intercept on the line $y=x$ by the circle ${ x }^{ 2 }+{ y }^{ 2 }-2x=0$ is $AB$. Equation of the circle with $AB$ as a diameter is
Question 7 :
Which of the following equations of a circle has center at (1, -3) and radius of 5?
Question 10 :
The radius of the circle with center (0,0) and which passes through (-6,8) is
Question 11 :
The equation to the circle with centre $(2,1)$ and touches the line $3x+4y-5$ is ?<br/>
Question 13 :
The equation ${ x }^{ 2 }+{ y }^{ 2 }=9$ meets x-axis at 
Question 15 :
The least value of $2x^{2} + y^{2} + 2xy + 2x - 3y + 8$ for real numbers $x$ and $y$ is
Question 16 :
The centre of the circle given by $\mathbf { r } \cdot ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } ) = 15 \text { and } | \mathbf { r } - ( \mathbf { j } + 2 \mathbf { k } ) | = 4 ,$
Question 17 :
The parabola $y = px^{2} + px + q$ is symmetrical about the line
Question 18 :
A circle has a diameter whose ends are at (-3, 2) and (12, -6) Its Equation is
Question 19 :
The equation of the circle passing through $(3, 6)$ and whose centre is $(2, -1)$ is
Question 20 :
What is the radius of the circle with the following equation?<br>$\displaystyle x^{2}-6x+y^{2}-4y-12=0$<br>
Question 21 :
If the vertices of a triangle are $(2, -2), (-1, -1)$ and $(5, 2)$ then the equation of its circumcircle is?
Question 22 :
Equation of the circle with centre on y-axis and passing through the points $(1,0),(1,1)$ is:
Question 24 :
The radius of the circle centred at $(4,5)$ and passing through the centre of the circle ${x}^{2}+{y}^{2}+4x+6y-12=0$ is
Question 25 :
Find the equation of a circle with center $(0, 0)$ and radius $5$.<br/>
Question 27 :
If the equation $ax^{2}+2(a^{2}+ab-16)xy+by^{2}2ax+2by-\sqrt[4]{2}=0$ represents a circle, the radius of the circle is
Question 28 :
The circle with radius $1$ and centre being foot of the perpendicular from $(5, 4)$ on y-axis, is?
Question 29 :
Find the value of a if $y^2=4ax $ pases through $(8,8)$
Question 30 :
State whether the following statements are true or false.<br/>The equation $x^{2}+y^{2} + 2x -10y + 30 = 0$ represents the equation of a circle.<br/>
Question 31 :
Find the equation of the circle passing through the origin and centre lies on the point of intersection of the lines $2x+y=3$ and $3x+2y=5$.
Question 32 :
Centres of the three circles<br/>${x}^{2}+{y}^{2}-4x-6y-14=0$ <br/>${x}^{2}+{y}^{2}+2x+4y-5=0$ and<br/>${x}^{2}+{y}^{2}-10x-16y+7=0$. The centres of the circles are:
Question 33 :
Assertion: If the equation of a circle is $(x+1)^2+(y-1)^2=4$, then its radius is 4.
Reason: Equation of a circle with radius r is given by, $(x-a)^2 + (y-b)^2=r^2$.
Question 34 :
Find the equation of the circle : <br>Centered at $(3,-2)$ with radius $4$.
Question 35 :
The one end of the latusrectum of the parabola ${ y }^{ 2 }-4x-2y-3=0$ is at
Question 36 :
If $(4,3)$ and $(-12,-1)$ are end points of a diameter of a circle, then the equation of the circle is-<br>
Question 37 :
Find the equation of the circle with center on x + y = 4 and 5x + 2y + 1 = 0 and having a radius of 3
Question 38 :
The length of the latus rectum of the parabola $x=ay^2+by+c$ is
Question 39 :
The length of the latus rectum of the parabola $169 \left[(x-1)^2+(y-3)^2\right]=(5x-12y+17)^2$ is:
Question 40 :
A circle is dawn its centre on the line $ x+y=2$ to touch the line $ 4x-3y+4=0$ and pass through the point $(0,1)$. Find the equation.
Question 41 :
A parabola with axis parallel to $x$ axis passes through $(0, 0), (2, 1), (4, -1).$ Its length of latus rectum is<br/>
Question 42 :
The line $(x-2)\cos \theta +(y-2)\sin \theta =1$ touches a circle for all value of $\theta$, then the equation of circle is
Question 43 :
The circle ${x^2} + {y^2} - 3x - 4y + 2 = 0$ cuts $x$-axis
Question 44 :
The equation of the tangent to the curve y = 2sinx + sin2x at $x=\frac { \pi }{ 3 } $ on it is
Question 45 :
The lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area $154$ sq.units. The equation of the circle is
Question 46 :
Assertion: The length of latus rectum of the parabola whose parametric equation is $\displaystyle x = t^{2} + t + 1$ & $\displaystyle y = t^{2} - t + 1$ for $\displaystyle t \: \in \: R$ is equal to $\displaystyle 2$.
Reason: The length of the latus rectum of the parabola $\displaystyle y^{2} = 4ax$ is $\displaystyle 4a$.
Question 47 :
Find the equation of a circle with center $(2,0)$ and passing through point $\left( 3,\sqrt { 3 }  \right) $. 
Question 48 :
The lines 2x-3y $=5$ and 3x-4y $=7$ diameters of a circle having area as $154$ units. Then the equation of the circle is:<br>
Question 49 :
The equation of a circle which has a tangent $3x+4y=6$ and two normals given by $(x-1)(y-2)=0$ is
Question 50 :
On the parabola $y={ x }^{ 2 }$, the point least distant from the straight line $y=2x-4$ is
Question 51 :
If the centroid of an equilateral triangle is $(1, 1)$ and its one vertex is $(-1, 2)$ then the equation of its circumcircle is
Question 52 :
The equation of a diameter of a circle is $x+y=1$ and the greatest distance of any point of the circle from the diameter is $\dfrac{1}{\sqrt{2}}$ .Then, a possible  equation of the circle can be
Question 53 :
If the circle $x^{2}+y^{2}=9$ passesthrough $(2,c)$ then $c$ is equal to 
Question 54 :
A circle is concentric with circle $x^{2}+ y^{2}-2x+4y-20=0$. If perimeter of the semicircle is $36$ then the equation of the circle is :
Question 55 :
If the tangent to the curve, $y=x^3+ax-b$ at the point $(1, -5)$ is perpendicular to the line, $-x+y+4=0$, then which one of the following points lies on the curve?
Question 56 :
If the lines $3x-4y-7=0$ and $2x-3y-5=0$ are two diameters of a circle of area 154 square units , the equation of the circle is :<br/><br/>
Question 57 :
Find the equation to the circle which touches the axis of $y$ at the origin and passes through the point $(b, c)$.
Question 58 :
The ends of the latus rectum of the conic $x^{2} + 10x - 16y + 25 = 0$ are
Question 59 :
The equation of the circle which touches x-axis at $(0,0)$ and touches the line $3x + 4y-  5 =0$ is<br/>
Question 60 :
The equation of the image of the circle $x^{2}+y^{2}-6x-4y+12=0$ by the line mirror $x+y-1=0$ is<br>
Question 61 :
A circle of radius $5$ units passes through the points $(7,1),(9,5)$. If the ordinate of the centre is less than $2$, then the equation of the circle is<br/>
Question 62 :
For the points on the circle $\displaystyle x^{2}+y^{2}-2x-2y+1=0$, the sum of maximum and minimum values of $4x + 3y$ is 
Question 63 :
The equation of the circle passing through $(2,0)$ and $(0,4)$ and having the minimum radius is
Question 64 :
The lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circel of area $154sq.$ units. Then the equation of circle is
Question 65 :
The equation of directrix and latus rectum of a parabola are $3x-4y+27=0$ and $3x-4y+2=0$. Then the length of latus rectum is <br>
Question 66 :
Which ordered number pair represents the center of the circle $x^2 + y^2 - 6x + 4y - 12 = 0$?
Question 67 :
Find the center-radius form of the equation of the circle with center $\left( 4,0 \right) $ and radius $7$
Question 68 :
Consider the parametric equation<br/>$x = \dfrac {a(1 - t^{2})}{1 + t^{2}}, y = \dfrac {2at}{1 + t^{2}}$.What does the equation represent?
Question 69 :
The vertex of the parabola $y^2 - 4y - x + 3 = 0$ is
Question 70 :
The circle passing through the points $(-1,0)$ and touching the y-axis at $(0,2)$ also passes through the point:
Question 71 :
Find the equation of the circle whose centre is the point of intersection of the lines $2x-3y+4=0$ and $3x+4y-5=0$ and passes through the origin.
Question 72 :
Equation of the circle with centre on the $y-$axis and passing through the origin and the point $(2,3)$ is
Question 73 :
The area of the circle represented by the equation ${(x+3)}^{2}+{(y+1)}^{2}=25$ is
Question 74 :
The equation $y^{2} + 4x + 4y + k = 0$ represents a parabola whose latus rectum is
Question 75 :
The length of the latus rectum of the parabola whose focus is $\left ( 3,3 \right )$ and directrix is  $3x-4y-2=0$ is<br/>
Question 76 :
The equation of the circle with centre $(2, 2)$ which passes through $(4,5)$ is
Question 78 :
The equation of the circle passing through $(3, 6)$ and whose centre is $(2, -1)$ is
Question 79 :
The circle ${ S }_{ 1 }$ with centre ${ C }_{ 1 }\left( { a }_{ 1 },{ b }_{ 1 } \right) $ and radius ${r}_{1}$ touches externally the circle ${S}_{2}$ with centre ${ C }_{ 2 }\left( { a }_{ 2 },{ b }_{ 2 } \right) $ and radius ${r}_{2}$. If the tangent at their common point passes through the origin then
Question 81 :
If the equation of the incircle of an equilateral triangle is ${ x }^{ 2 }+{ y }^{ 2 }+4x-6y+4=0$, then the equation of the circumcircle of the triangle is
Question 82 :
The normal at the point $(3, 4)$ on a circle cuts the circle again at the point $(1, 2)$. Then the equation of the circle is -
Question 83 :
The length of the latus rectum of the parabola whose vertex is $(2, -3)$ and the directrix $x = 4$ is
Question 84 :
If the straight line $y=mx+c$ is parallel to the axis of the parabola $y^2=lx$ and intersects the parabola at $\left(\dfrac{c^2}{8}, c\right)$ then the length of the latus rectum is 
Question 85 :
The product of perpendicular drawn from the origin to the lines represented by the equation $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$, will be:
Question 86 :
The locus of the point $(h,k)$, if the point $(\sqrt{3h}, \sqrt{3k + 2})$  lies on the line $x - y - 1 = 0$, is a ?
Question 87 :
The centre of a circle is $(2, -3)$ and the circumference is $10\pi$. Then, the equation of the circle is
Question 89 :
The graph of the curve $x^2 + y^2 - 2xy - 8x - 8y + 32 = 0$ falls wholly in the
Question 90 :
The equation of the circle passing through the points $(4, 1), (6, 5)$ and having the centre on the line $4x+y-16=0$ is 
Question 91 :
Locus of the point $(\sqrt{3h} , \sqrt{3k + 2} )$ if it lies on the line $x- y- 1 = 0$ is a
Question 93 :
A circle touches the y-axis at $(0, 2)$ and has an intercept of $4$ units on the positive side of the x-axis. Then the equation of the circle is?
Question 94 :
The arrangement of the following parabolas in the ascending order of their length of latusrectum <br/>A)   $y=4x^{2}+x+1$     B) $2y=x^{2}+x+5$<br/>C)   $x=2y^{2}+y+3$     D) $y^{2}+x+y+9=0$<br/>
Question 95 :
The length of latus rectum of the parabola whose parametric equations are $ x = t^{2} + t + 1$, $y = t^{2}-  t + 1$, where $t \in R$, is equal to?<br/>
Question 96 :
The circle passing through $\left(t,1\right),\left(1,t\right)$ and $\left(t,t\right)$ for all values of $t$ also passes through
Question 97 :
From the point $A\left(0,3\right)$ on the circle ${x}^{2}-4x+{\left(y-3\right)}^{2}=0$ a chord $AB$ is drawn and extended to a point $M$ such that $AM=2AB$.The locus is
Question 98 :
Find the equation of the circle with center at $(-3,5)$ and passes through the point $(5,-1)$
Question 99 :
Assertion: The length of latus rectum of the parabola $\displaystyle \left ( 3x - 4y + 2 \right )^{2} = 40\left ( 4x + 3y - 5 \right )$ is $\displaystyle 16$.
Reason: The length of latus rectum of the parabola $\displaystyle \left ( y - 2 \right )^{2} = 16 \left ( x + 3 \right )$ is $\displaystyle 16$.
Question 100 :
$f(\displaystyle \mathrm{m}_{\mathrm{i}}, \frac{1}{\mathrm{m}_{\mathrm{i}}})$ , $\mathrm{i}=1,2,3,4$ are four distinct points on the circle with centre origin, then value of $\mathrm{m}_{1}\mathrm{m}_{2}\mathrm{m}_{3}\mathrm{m}_{4}$ is equal to<br>
Question 101 :
The set of points $(x, y)$ whose distance from the line $y = 2x + 2$ is the same as the distance from $(2, 0)$ is a parabola. This parabola is congruent to the parabola in standard form $y = Kx^{2}$ for some $K$ which is equal to
Question 102 :
The curve described parametrically by$x = {t^2} + t + 1$ and $y = {t^2} - t + 1$ represents
Question 103 :
Find the equation of the circle that passes through the points $(0,6),(0,0)$ and $(8,0)$
Question 104 :
A thin rod of length $l$ in the shape of a semicircle is pivoted at one of its ends such that it is free to oscillate in its own plane. The frequency $f$ of small oscillations of the semicircular rod is :
Question 105 :
If the line $3x+4y=24$ and $4x+3y=24$ intersects the coordinates axes at $A,B,C$ and $D$, then the equation of the circle passing through these $4$ points  is<br/>
Question 106 :
If $16{m}^{2}-8l-1=0,$ then equation of the circle having $lx+my+1=0$ is a tangent is
Question 107 :
If $x=2+3\cos\theta$ and $y=1-3\sin\theta$ represent a circle then the centre and radius is?
Question 108 :
The radius of the circle $x^{2} + y^{2} + 4x + 6y + 13 = 0$ is
Question 110 :
The circle $x^{2}+y^{2}-8x=0$ and hyperbola $\dfrac{x^{2}}{9}-\dfrac{y^{2}}{4}=1$ intersect at the points $A$ and $B$.<br/>then the equation of the circle with $AB$ as its diameter is<br/>
Question 111 :
A circle touches the $x$-axis and also touches the circle with centre $(0, 3)$ and radius $2$. The locus of the centre of the circle is -
Question 112 :
The equation of a straight line drawn through the focus of the parabola $y^2=-4x$ at an angle of $120^o$ to the $x$-axis is.<br/>
Question 113 : <p>In the $xy$ plane, the segment with end points$(3,8)$ and $(<br>5,2)$ is the diameter of the circle. The point $(k,10)$ lies on the circle for:</p>
Question 114 :
A point $P(x, y)$ moves in $XY$ plane such that $x = a\cos^2 \theta$ and $y = 2a \sin \theta$, where $\theta$ is a parameter. The locus of the point $P$ is
Question 115 :
If two distinct chords of a parabola $x^2\, =\, 4ay$ passing through $(2a, a)$ are bisected on the line $x + y = 1$, then length of latus rectum can be
