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1
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
$3 \sqrt{6} x-y=21$
2
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
$\left(k_1-\frac{\sqrt{3} e}{2}\right)$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola $$x^2-y^2=a^2$$ is

A
$$y^4-x^4=4 a^2 x^2 y^2$$
B
$$y^2-x^2=4 a^2 x^2 y^2$$
C
$$a^2\left(y^2-x^2\right)=4 x^2 y^2$$
D
$$y^2+x^2=4 a^2 x^2 y^2$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$e_1$$ and $$e_2$$ are the eccentricities of the hyperbola $$16 x^2-9 y^2=1$$ and its conjugate respectively. Then, $$3 e_1=$$

A
$$5 e_2$$
B
$$4 e_2$$
C
$$2 e_2$$
D
$$ e_2$$
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