Test Details

Conic Sections

Jan 10, 8:00 PM

30 minutes

Jan 10, 8:30 PM

32.0 marks

MCQ

20 questions

Ranjeet Sharma

I am passionate about my work. my focus is on Conceptual clarity.

Class Details

Maths

Class 11th

Maths

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Question Text

Question 2 :
Equation of the circle with centre on y-axis and passing through the points $(1,0),(1,1)$ is:

Question 4 :
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 5 :
State the following statement is True or FalseIf a quadratic function $f(x)=ax^2+bx+c$ has a downward parabola then $a > 0$.

Question 7 :
The length of the diameter of the circle ${x^2} + {y^2} - 4x - 6y + 4 = 0$

Question 8 :
The circle with radius $1$ and centre being foot of the perpendicular from $(5, 4)$ on y-axis, is?

Question 9 :
The equation of the ellipse whose foci are $(\pm5,0)$ and of the directrix is $5x=36$, is

Question 10 :
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 11 :
The area of an ellipse is $ 8\pi$ sq. units. Its distance between the foci is $4\sqrt{3}$, then $\mathrm{e}=$

Question 12 :
The ellipse $\displaystyle \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ passes through the point $\displaystyle \left ( -3, \: 1 \right )$ and has the eccentricity $\displaystyle \sqrt{\frac{2}{5}}$. Then the major axis of the ellipse has the length:

Question 13 :
If (5,12) and (24,7) are the foci of a hyperbola passing through the origin, then

Question 14 :
A focus of an ellipse is at the origin. The directrix is the line $\mathrm{x}=4$ and the eccentricity is $\displaystyle \frac{1}{2}$. Then the length of the semi major axis is

Question 15 :
$P$ is a point on the ellipse having $(3,4)$ and $(3,-2)$ as the ends of minor axis. If the sum of the focal distances of $P$ be equal to $10$ then its equation is

Question 16 :
If the eccentricity of an ellipse is $\dfrac58$ and the distance between its foci is $10$, then its latus rectum is

Question 17 :
A circle is described with minor axis of the ellipse as diameter. If the foci lie on the circle, then the eccentricty of the ellipse is

Question 18 :
If (5,12) and (24,7) are the foci of a conic passing through the origin then the eccentricity of conic is

Question 19 :
If the normal at the end of latus rectum of the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ passes through $(0, -b)$, then $e^4+e^2$ (where $E$ is eccentricity) equals

Question 20 :
The point P on the parabola $y^2= 4ax$ for which |PR PQ| is maximum, where R $ ( -a , 0)$, Q $ (0 , a)$, is

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