1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex, then $\theta=$
A
$45^{\circ}$
B
$90^{\circ}$
C
$135^{\circ}$
D
$60^{\circ}$
2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the ellipse $4 x^2+9 y^2=36$ is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hyperbola lie on the circle
A
$x^2+y^2=81$
B
$x^2+y^2=16$
C
$x^2+y^2=25$
D
$x^2+y^2=5$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\sec \alpha$, then area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is
A
$a^2 b^2 \sec ^2 \alpha$
B
$\frac{b^2}{|\tan \alpha|}$
C
$a^2 \tan ^2 \alpha$
D
$\left(a^2+b^2\right) \tan ^2 \alpha$
4
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $e_1$ and $e_2$ are respectively the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conjugate hyperbola, then the line $\frac{x}{2 e_1}+\frac{y}{2 e_2}=1$ touches the circle having centre at the origin, then its radius is

A
2
B
$e_1+e_2$
C
$e_1 e_2$
D
4
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