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1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $e_1$ and $e_2$ are respectively the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conjugate hyperbola, then the line $\frac{x}{2 e_1}+\frac{y}{2 e_2}=1$ touches the circle having centre at the origin, then its radius is

A
2
B
$e_1+e_2$
C
$e_1 e_2$
D
4
2
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The descending order of magnitude of the eccentricities of the following hyperbolas is A. A hyperbola whose distance between foci is three times the distance between its directrices. B. Hyperbola in which the transverse axis is twice the conjugate axis. C. Hyperbola with asymptotes $x+y+1=0, x-y+3=0$
A
$C, A, B$
B
B, C, A
C
C, B, A
D
A, C, B
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The equation of the pair of asymptotes of the hyperbola $4 x^2-9 y^2-24 x-36 y-36=0$ is
A
$2 x^2-x y-3 y^2-14 x-9 y-12=0$
B
$2 x^2-x y-3 y^2-2 x+3 y=0$
C
$2 x^2-5 x y+3 y^2-22 x+27 y+60=0$
D
$4 x^2-9 y^2-24 x-36 y=0$
4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The equation of one of the tangents drawn from the point $(0,1)$ to the hyperbola $45 x^2-4 y^2=5$ is
A
$4 y+5=0$
B
$3 x+4 y-4=0$
C
$5 x-6 y+6=0$
D
$9 x-2 y+2=0$
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