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1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the equation of the hyperbola having $(8,3),(0,3)$ as foci and $\frac{4}{3}$ as eccentricity is $\frac{(x-\alpha)^2}{p}-\frac{(y-\beta)^2}{q}=1$, then $p+q=$

A

$\beta^2$

B

$\alpha+\beta$

C

$\alpha^2$

D

$\alpha \beta$

2
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $y=x+\sqrt{2}$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{2}=1$, then equations of its directrices are
A
$x= \pm \sqrt{3}$
B
$x= \pm \sqrt{\frac{8}{3}}$
C
$x= \pm \sqrt{\frac{2}{3}}$
D
$x= \pm \sqrt{\frac{4}{3}}$
3
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The area of the quadrilateral formed with the foci of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ and its conjugate hyperbola is (in sq units)
A
24
B
25
C
16
D
50
4
AP EAPCET 2024 - 22th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The line $21 x+5 y=k$ touches the hyperbola $7 x^2-5 y^2=232$, then $k$ is equal to
A
116
B
232
C
$58^{\prime}$
D
110
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