1
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The slope of the tangent drawn from the point $(1,1)$ to the hyperbola $2 x^2-y^2=4$ is
A
2
B
$\frac{-2 \pm \sqrt{6}}{2}$
C
$-1 \pm \sqrt{6}$
D
$\frac{-2 \pm \sqrt{3}}{2}$
2
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9 x^2-16 y^2=144$. If $p>0$ and $q>0$, then $q=$
A
$\frac{9}{4}$
B
$\frac{7}{4}$
C
$\frac{15}{4}$
D
$\frac{13}{4}$
3
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
4
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
$-\left(\frac{a^2+b^2}{b}\right)$
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