1
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $(1,3)$ is the mid-point of a chord of the circle $x^2+y^2-4 x-8 y+16=0$, then the area of the triangle formed by that chord with the coordinate axes is
A
16
B
8
C
4
D
$8 \sqrt{2}$
2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the circles $x^2+y^2+2 \alpha x+2 y-8=0$ and $x^2+y^2-2 x+a y-14=0$ intersect orthogonally, then the distance between their centres is
A
$\sqrt{242}$
B
$\sqrt{970}$
C
$\sqrt{629}$
D
$\sqrt{541}$
3
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
$y^2=9(x-3)$
4
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
$5 / 12$
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