Hyperbola · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1
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
AP EAPCET 2024 - 23th May Morning Shift
2
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)
AP EAPCET 2024 - 23th May Morning Shift
3
The line $21 x+5 y=k$ touches the hyperbola $7 x^2-5 y^2=232$, then $k$ is equal to
AP EAPCET 2024 - 22th May Evening Shift
4
If the equation $\frac{x^2}{7-k}+\frac{y^2}{5-k}=1$ represents a hyperbola, then
AP EAPCET 2024 - 22th May Evening Shift
5

The transformed equation of $x^2-y^2+2 x+4 y=0$ when the origin is shifted to the point $(-1,2)$ is

AP EAPCET 2024 - 22th May Morning Shift
6
If the ellipse $4 x^2+9 y^2=36$ is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hyperbola lie on the circle
AP EAPCET 2024 - 22th May Morning Shift
7
If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\sec \alpha$, then area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is
AP EAPCET 2024 - 22th May Morning Shift
8

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

AP EAPCET 2024 - 22th May Morning Shift
9
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 $x+y+1=0, x-y+3=0$
AP EAPCET 2024 - 21th May Evening Shift
10
The equation of the pair of asymptotes of the hyperbola $4 x^2-9 y^2-24 x-36 y-36=0$ is
AP EAPCET 2024 - 21th May Morning Shift
11
The equation of one of the tangents drawn from the point $(0,1)$ to the hyperbola $45 x^2-4 y^2=5$ is
AP EAPCET 2024 - 21th May Morning Shift
12
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
13
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
14
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
15
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
16
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
17
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
18
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
19
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
20

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
21

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
22

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
23

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
24

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

AP EAPCET 2022 - 4th July Morning Shift
25

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
26

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
27

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
28

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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