Hyperbola · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1
If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2 \sqrt{3})$ is $\sqrt{5} x=4$ and e is its eccentricity, then $e^2=$
AP EAPCET 2024 - 20th May Evening Shift
2
If $l_1$ and $l_2$ are the lengths of the perpendiculars drawn from a point on the hyperbola $5 x^2-4 y^2-20=0$ to its asymptotes, then $\frac{l_1{ }^2 l_2{ }^2}{100}=$
AP EAPCET 2024 - 20th May Evening Shift
3
If a circle of radius 4 cm passes through the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ and concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is
AP EAPCET 2024 - 20th May Morning Shift
4
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
AP EAPCET 2024 - 20th May Morning Shift
5
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
AP EAPCET 2024 - 19th May Evening Shift
6
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 $b^2=$
AP EAPCET 2024 - 19th May Evening Shift
7
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
AP EAPCET 2024 - 18th May Morning Shift
8
If the angle between the asymptotes of the hyperbola $x^2-k y^2=3$ is $\frac{\pi}{3}$ and $e$ is its eccentricity, then the pole of the line $x+y-1=0$ with respect to this hyperbola is
AP EAPCET 2024 - 18th May Morning Shift
9

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola $$x^2-y^2=a^2$$ is

AP EAPCET 2022 - 5th July Morning Shift
10

If $$e_1$$ and $$e_2$$ are the eccentricities of the hyperbola $$16 x^2-9 y^2=1$$ and its conjugate respectively. Then, $$3 e_1=$$

AP EAPCET 2022 - 5th July Morning Shift
11

If the normal to the rectangular hyperbola $$x^2-y^2=1$$ at the point $$P(\pi / 4)$$ meets the curve again at $$Q(\theta)$$, then $$\sec ^2 \theta+\tan \theta=$$

AP EAPCET 2022 - 4th July Evening Shift
12

If the vertices and foci of a hyperbola are respectively $$( \pm 3,0)$$ and $$( \pm 4,0)$$, then the parametric equations of that hyperbola are

AP EAPCET 2022 - 4th July Evening Shift
13

The value of $$\frac{1+\tan \mathrm{h} x}{1-\tan \mathrm{h} x}$$ is

AP EAPCET 2022 - 4th July Morning Shift
14

Let origin be the centre, $$( \pm 3,0)$$ be the foci and $$\frac{3}{2}$$ be the eccentricity of a hyperbola. Then, the line $$2 x-y-1=0$$

AP EAPCET 2022 - 4th July Morning Shift
15

The locus of a variable point whose chord of contact w.r.t. the hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$ subtends a right angle at the origin is

AP EAPCET 2022 - 4th July Morning Shift
16

If one focus of a hyperbola is $$(3,0)$$, the equation of its directrix is $$4 x-3 y-3=0$$ and its eccentricity $$e=5 / 4$$, then the coordinates of its vertex is

AP EAPCET 2021 - 20th August Morning Shift
17

The asymptotes of the hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$, with any tangent to the hyperbola form a triangle whose area is $$a^2 \tan (\alpha)$$. Then, its eccentricity equals

AP EAPCET 2021 - 19th August Morning Shift
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