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
55
MCQ (Single Correct Answer)
The length of the latusrectum of the ellipse $3 x^2+y^2=12$ is
A
4
B
3
C
8
D
$\frac{4}{\sqrt3}$
56
MCQ (Single Correct Answer)
If $e$ is eccentricity of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1($ where, $a
A
$b^2=a^2\left(1-e^2\right)$
B
$a^2=b^2\left(1-e^2\right)$
C
$a^2=b^2\left(e^2-1\right)$
D
$b^2=a^2\left(e^2-1\right)$
57
MCQ (Single Correct Answer)
The eccentricity of the hyperbola whose latusrectum is 8 and conjugate axis is equal to half of the distance between the foci is
A
$\frac{4}{3}$
B
$\frac{4}{\sqrt{3}}$
C
$\frac{2}{\sqrt{3}}$
D
None of these