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
58
MCQ (Single Correct Answer)
The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$. Its equation is
A
$x^2-y^2=32$
B
$\frac{x^2}{4}-\frac{y^2}{9}=1$
C
$2 x-3 y^2=7$
D
None of these
59
MCQ (Single Correct Answer)
Equation of the hyperbola with eccentricity $\frac{3}{2}$ and foci at $( \pm 2,0)$ is
A
$\frac{x^2}{4}-\frac{y^2}{5}=\frac{4}{9}$
B
$\frac{x^2}{9}-\frac{y^2}{9}=\frac{4}{9}$
C
$\frac{x^2}{4}-\frac{y^2}{9}=1$
D
None of these