Test Details

Conic Sections

Test

Feb 01, 3:13 PM

60 minutes

Feb 01, 4:13 PM

30.0 marks

MCQ

30 questions

SURYA KANT SHARMA

...

Class Details

Maths

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Question Text

Question 1 :
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 2 :
The parabola $y = px^{2} + px + q$ is symmetrical about the line

Question 3 :
Find the equation of the circle : Centered at $(3,-2)$ with radius $4$.

Question 4 :
Find the equation of a circle with center $(0, 0)$ and radius $5$.

Question 5 :
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 6 :
The equation of the circle passing through $(3, 6)$ and whose centre is $(2, -1)$ is

Question 8 :
Centres of the three circles ${x}^{2}+{y}^{2}-4x-6y-14=0$  ${x}^{2}+{y}^{2}+2x+4y-5=0$ and ${x}^{2}+{y}^{2}-10x-16y+7=0$. The centres of the circles are:

Question 9 :
Equation of the circle with centre on y-axis and passing through the points $(1,0),(1,1)$ is:

Question 10 :
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 11 :
If the vertices of a triangle are $(2, -2), (-1, -1)$ and $(5, 2)$ then the equation of its circumcircle is?

Question 13 :
A circle has a diameter whose ends are at (-3, 2) and (12, -6) Its Equation is

Question 15 :
The least value of $2x^{2} + y^{2} + 2xy + 2x - 3y + 8$ for real numbers $x$ and $y$ is

Question 17 :
What is the radius of the circle with the following equation? $\displaystyle x^{2}-6x+y^{2}-4y-12=0$

Question 18 :
State whether the following statements are true or false. The equation $x^{2}+y^{2} + 2x -10y + 30 = 0$ represents the equation of a circle.

Question 19 :
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 20 :
The radius of the circle with center (0,0) and which passes through (-6,8) is

Question 21 :
The circle with radius $1$ and centre being foot of the perpendicular from $(5, 4)$ on y-axis, is?

Question 23 :
The length of the diameter of the circle ${x^2} + {y^2} - 4x - 6y + 4 = 0$

Question 24 :
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 27 :
Find the value of a if $y^2=4ax $ pases through $(8,8)$

Question 29 :
Which of the following equations of a circle has center at (1, -3) and radius of 5?

Question 30 :
The equation ${ x }^{ 2 }+{ y }^{ 2 }=9$ meets x-axis at 

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