1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The line $x-2 y-3=0$ cuts the parabola $y^2=4 \operatorname{ar}$ at the points $P$ and $Q$. If the focus of this parabola is $\left(\frac{1}{4}, k\right)$. then $P Q=$
A
$16 a \sqrt{5}$
B
$8 a \sqrt{5}$
C
$4 a \sqrt{5}$
D
$2 a \sqrt{5}$
2
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $4 x-3 y-5=0$ is a normal to the ellipse $3 x^2+8 y^2=k$, then the equation of the tangent drawn to this ellipse at the point $(-2, m)(m>0)$ is
A
$3 x+4 y-14=0$
B
$3 x-4 y+10=0$
C
$3 x-4 y+1=0$
D
$4 x+3 y-3=0$
3
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the line $5 x-2 y-6=0$ is a tangent to the hyperbola $5 x^2-k y^2=12$, then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)(p<0)$ is
A
$\sqrt{6} x+2 y=0$
B
$2 \sqrt{6} x+3 y=3$
C
$\sqrt{6} x-5 y=21$
D
$3 \sqrt{6} x-y=21$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity, then the pole of the line $x+y-1=0$ with respect to this hyperbola is
A
$\left(k, \frac{\sqrt{30}}{2}\right)$
B
$\left(-k, \frac{\sqrt{3} e}{2}\right)$
C
$\left(-k,-\frac{\sqrt{3} e}{2}\right)$
D
$\left(k_1-\frac{\sqrt{3} e}{2}\right)$
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