1
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the equation $x+y+n=0$ represents a normal to the hyperbola $\frac{x^2}{6}-\frac{y^2}{2}=1$, then $n=$

A

$\pm \sqrt{3}$

B

$\pm 4$

C

$\pm \sqrt{2}$

D

$\pm 2$

2
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $y=m x+4(m>0)$ is a tangent to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$, then the point of contact of this tangent is

A

$\left(-\frac{25}{4},-\frac{9}{4}\right)$

B

$\left(\frac{25}{4}, \frac{9}{4}\right)$

C

$(1,5)$

D

$\left(-\frac{1}{2}, \frac{7}{2}\right)$

3
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
$-\left(\frac{a^2+b^2}{b}\right)$
4
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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