50
MCQ (Single Correct Answer)
The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length $3 a$ is
A
$x^2+y^2=9 a^2$
B
$x^2+y^2=16 a^2$
C
$x^2+y^2=4 a^2$
D
$x^2+y^2=a^2$
51
MCQ (Single Correct Answer)
If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$, then its equation is
A
$x^2=-12 y$
B
$x^2=12 y$
C
$y^2=-12 x$
D
$y^2=12 x$
52
MCQ (Single Correct Answer)
If the parabola $y^2=4 a x$ passes through the point $(3,2)$, then the length of its latusrectum is
A
$\frac{2}{3}$
B
$\frac{4}{3}$
C
$\frac{1}{3}$
D
4
53
MCQ (Single Correct Answer)
If the vertex of the parabola is the point $(-3,0)$ and the directrix is the line $x+5=0$, then its equation is
A
$y^2=8(x+3)$
B
$x^2=8(y+3)$
C
$y^2=-8(x+3)$
D
$y^2=8(x+5)$
54
MCQ (Single Correct Answer)
If equation of the ellipse whose focus is $(1,-1)$, then directrix the line $x-y-3=0$ and eccentricity $\frac{1}{2}$ is
A
$7 x^2+2 x y+7 y^2-10 x+10 y+7=0$
B
$7 x^2+2 x y+7 y^2+7=0$
C
$7 x^2+2 x y+7 y^2+10 x-10 y-7=0$
D
None of the above