1
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The point of intersection of two tangents drawn to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ lie on the circle $x^2+y^2=5$. If these tangents are perpendicular to each other, then $a=$
A
25
B
5
C
9
D
3
2
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ are two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ where, $\phi+\theta=\frac{\pi}{2}$. If $(h, k)$ is the point of intersection of the normals drawn at $P$ and $Q$, then $k=$

A
$\frac{a^2-b^2}{b}$
B
$\frac{a^2+b^2}{b}$
C
$-\left(\frac{a^2-b^2}{b}\right)$
D
$-\left(\frac{a^2+b^2}{b}\right)$
3
TS EAMCET 2023 (Online) 12th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the equation of a hyperbola is $9 x^2-16 y^2+72 x-32 y-16=0$, then the equation of conjugate hyperbola is
A
$9 x^2-16 y^2+72 x-32 y+272=0$
B
$9 x^2-16 y^2+72 x-32 y+288=0$
C
$9 x^2-16 y^2+72 x-32 y-38=0$
D
$9 x^2-16 y^2+72 x-32 y+16=0$
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