1
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If a tangent to the hyperbola $x^2-\frac{y^2}{3}=1$ is also a tangent to the parabola $y^2=8 x$, then equation of such tangent with the positive slope is
A
$y-x-\frac{1}{2}=0$
B
$y-2 x-1=0$
C
$2 y-4 x-1=0$
D
$y-x-1=0$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
The locus of the mid-points of the chords of the hyperbola $x^2-y^2=a^2$ which touch the parabola $y^2=4 a x$ is
A
$x\left(y^2-x^2\right)=a y^2$
B
$x\left(x^2+y^2\right)=y^2+x$
C
$a x^3+y^3=3 x$
D
$x\left(x^2-y^2\right)=a^2$
3
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If the product of eccentricities of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=-1$ is 1 , then $b^2=$
A
$\frac{12}{25}$
B
144
C
25
D
$\frac{144}{25}$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the line $5 x-2 y-6=0$ is a tangent to the hyperbola $5 x^2-k y^2=12$, then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)(p<0)$ is
A
$\sqrt{6} x+2 y=0$
B
$2 \sqrt{6} x+3 y=3$
C
$\sqrt{6} x-5 y=21$
D
$3 \sqrt{6} x-y=21$
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