1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12 x$ and a point on the parabola in the ratio $1: 2$. Then, the locus of $p$ is

A
$y^2=2(x-2)$
B
$y^2=4 x$
C
$y^2=4(x-2)$
D
$y^2=9(x-3)$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $T_1$ be the tangent drawn at a point $P(\sqrt{2}, \sqrt{3})$ on the ellipse $\frac{x^2}{4}+\frac{y^2}{6}=1$. If ( $\alpha, \beta$ ) is the point where, $T_1$ intersects another tangent $T_2$ to the ellipse perpendicularly, then $\alpha^2+\beta^2$ is equal to
A
10
B
52
C
26
D
$5 / 12$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=x+\sqrt{2}$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{2}=1$, then equations of its directrices are
A
$x= \pm \sqrt{3}$
B
$x= \pm \sqrt{\frac{8}{3}}$
C
$x= \pm \sqrt{\frac{2}{3}}$
D
$x= \pm \sqrt{\frac{4}{3}}$
4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The area of the quadrilateral formed with the foci of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ and its conjugate hyperbola is (in sq units)
A
24
B
25
C
16
D
50
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