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Previous year question hub

Hyperbola - Coordinate Geometry PYQs (Math)

Practice Hyperbola previous year questions for AP EAPCET Math. 55 PYQs from 30 papers across 5 years. Topic-wise coordinate geometry practice test.

30Papers
5Years
55Questions
1Topics

Hyperbola question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Hyperbola. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 62 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 62 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
55 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
55 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Hyperbola
55 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

AP EAPCET 2025 22ND MAY MORNING SHIFT
3 Qs
AP EAPCET 2025 21ST MAY EVENING SHIFT
2 Qs
AP EAPCET 2025 21ST MAY MORNING SHIFT
2 Qs
AP EAPCET 2025 22ND MAY EVENING SHIFT
2 Qs
AP EAPCET 2025 23RD MAY EVENING SHIFT
2 Qs
AP EAPCET 2025 23RD MAY MORNING SHIFT
2 Qs
AP EAPCET 2025 24TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2025 26TH MAY EVENING SHIFT
2 Qs
AP EAPCET 2025 26TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2025 27TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2024 22TH MAY MORNING SHIFT
4 Qs
AP EAPCET 2024 18TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2024 19TH MAY EVENING SHIFT
2 Qs
AP EAPCET 2024 20TH MAY EVENING SHIFT
2 Qs
AP EAPCET 2024 20TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2024 21TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2024 22TH MAY EVENING SHIFT
2 Qs
AP EAPCET 2024 23TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2024 21TH MAY EVENING SHIFT
1 Qs
AP EAPCET 2023 - 15th May Evening Shift
3 Qs
AP EAPCET 2023 - 15th May Evening Shift
3 Qs
AP EAPCET 2023 - 15th May Morning Shift
2 Qs
AP EAPCET 2023 - 15th May Morning Shift
2 Qs
AP EAPCET 2023 - 15th May Morning Shift
2 Qs
AP EAPCET 2022 4TH JULY MORNING SHIFT
3 Qs
AP EAPCET 2022 4TH JULY EVENING SHIFT
2 Qs
AP EAPCET 2022 5TH JULY MORNING SHIFT
2 Qs
AP EAPCET 2021 19TH AUGUST MORNING SHIFT
1 Qs
AP EAPCET 2021 20TH AUGUST EVENING SHIFT
1 Qs
AP EAPCET 2021 20TH AUGUST MORNING SHIFT
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
AP EAPCET 2025 21ST MAY EVENING SHIFT20252View paper
AP EAPCET 2025 21ST MAY MORNING SHIFT20252View paper
AP EAPCET 2025 22ND MAY EVENING SHIFT20252View paper
AP EAPCET 2025 22ND MAY MORNING SHIFT20253View paper
AP EAPCET 2025 23RD MAY EVENING SHIFT20252View paper
AP EAPCET 2025 23RD MAY MORNING SHIFT20252View paper
AP EAPCET 2025 24TH MAY MORNING SHIFT20252View paper
AP EAPCET 2025 26TH MAY EVENING SHIFT20252View paper
AP EAPCET 2025 26TH MAY MORNING SHIFT20252View paper
AP EAPCET 2025 27TH MAY MORNING SHIFT20252View paper
AP EAPCET 2024 18TH MAY MORNING SHIFT20242View paper
AP EAPCET 2024 19TH MAY EVENING SHIFT20242View paper
AP EAPCET 2024 20TH MAY EVENING SHIFT20242View paper
AP EAPCET 2024 20TH MAY MORNING SHIFT20242View paper
AP EAPCET 2024 21TH MAY EVENING SHIFT20241View paper
AP EAPCET 2024 21TH MAY MORNING SHIFT20242View paper
AP EAPCET 2024 22TH MAY EVENING SHIFT20242View paper
AP EAPCET 2024 22TH MAY MORNING SHIFT20244View paper
AP EAPCET 2024 23TH MAY MORNING SHIFT20242View paper
AP EAPCET 2023 - 15th May Evening Shift20233View paper
AP EAPCET 2023 - 15th May Evening Shift20233View paper
AP EAPCET 2023 - 15th May Morning Shift20232View paper
AP EAPCET 2023 - 15th May Morning Shift20232View paper
AP EAPCET 2023 - 15th May Morning Shift20232View paper
AP EAPCET 2022 4TH JULY EVENING SHIFT20222View paper
AP EAPCET 2022 4TH JULY MORNING SHIFT20223View paper
AP EAPCET 2022 5TH JULY MORNING SHIFT20222View paper
AP EAPCET 2021 19TH AUGUST MORNING SHIFT20211View paper
AP EAPCET 2021 20TH AUGUST EVENING SHIFT20211View paper
AP EAPCET 2021 20TH AUGUST MORNING SHIFT20211View paper

All Hyperbola previous year questions

Practice every matching question in batches of 20, with every available option.

1
2021 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2021 19TH AUGUST MORNING SHIFT

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

A
\(\sec (\alpha)\)
B
\(\operatorname{cosec}(\alpha)\)
C
\(\sec ^2(\alpha)\)
D
\(\operatorname{cosec}^2(\alpha)\)
Open complete paper
2
2021 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2021 20TH AUGUST EVENING SHIFT

If the focal chord of the hyperbola subtends a right angle at the center, then its eccentricity is

A
\(e=\frac{\sqrt{3}-1}{2}\)
B
\(e=\frac{\sqrt{5}-1}{2}\)
C
\(e=\frac{\sqrt{5}+1}{2}\)
D
\(e=\frac{\sqrt{3}+1}{2}\)
Open complete paper
3
2021 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2021 20TH AUGUST MORNING SHIFT

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

A
\(\left(\frac{3}{5}, \frac{11}{5}\right)\)
B
\(\left(\frac{11}{5}, \frac{3}{5}\right)\)
C
\(\left(\frac{7}{5}, \frac{4}{5}\right)\)
D
\(\left(\frac{4}{5}, \frac{7}{5}\right)\)
Open complete paper
4
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 4TH JULY EVENING SHIFT

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 \(\sec ^2 \theta+\tan \theta=\)

A
43
B
57
C
3
D
1
Open complete paper
5
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 4TH JULY EVENING SHIFT

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

A
\(x=3 \sec \theta, y=7 \tan \theta\)
B
\(x=\sqrt{3} \sec \theta, y=\sqrt{7} \tan \theta\)
C
\(x=\sqrt{3} \sec \theta, y=7 \tan \theta\)
D
\(x=3 \sec \theta, y=\sqrt{7} \tan \theta\)
Open complete paper
6
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 4TH JULY MORNING SHIFT

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

A
intersects the hyperbola at two points.
B
does not intersect the hyperbola.
C
touches the hyperbola.
D
passes through the vertex of the hyperbola.
Open complete paper
7
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 4TH JULY MORNING SHIFT

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

A
\(e^x\)
B
\(e^{-2 x}\)
C
\(e^{2 x}\)
D
\(e^{-x}\)
Open complete paper
8
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 4TH JULY MORNING SHIFT

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

A
\(\frac{x^2}{4 a^2}-\frac{y^2}{4 b^2}=1\)
B
\(\left(\frac{x^2}{a^2}-\frac{y^2}{b^2}\right)=\frac{x^2}{a^4}+\frac{y^2}{b^4}\)
C
\(\frac{x}{a}-\frac{y}{b}=\frac{1}{a^2}+\frac{1}{b^2}\)
D
\(\frac{x^2}{a^4}+\frac{y^2}{b^4}=\frac{1}{a^2}-\frac{1}{b^2}\)
Open complete paper
9
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 5TH JULY MORNING SHIFT

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

A
\(5 e_2\)
B
\(4 e_2\)
C
\(2 e_2\)
D
\(e_2\)
Open complete paper
10
2022 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2022 5TH JULY MORNING SHIFT

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

A
\(y^4-x^4=4 a^2 x^2 y^2\)
B
\(y^2-x^2=4 a^2 x^2 y^2\)
C
\(a^2\left(y^2-x^2\right)=4 x^2 y^2\)
D
\(y^2+x^2=4 a^2 x^2 y^2\)
Open complete paper
11
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 18TH MAY MORNING SHIFT
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
$3 \sqrt{6} x-y=21$
Open complete paper
12
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 18TH MAY MORNING SHIFT
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
A
$\left(k, \frac{\sqrt{30}}{2}\right)$
B
$\left(-k, \frac{\sqrt{3} e}{2}\right)$
C
$\left(-k,-\frac{\sqrt{3} e}{2}\right)$
D
$\left(k_1-\frac{\sqrt{3} e}{2}\right)$
Open complete paper
13
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 19TH MAY EVENING SHIFT
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
$x\left(x^2-y^2\right)=a^2$
Open complete paper
14
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 19TH MAY EVENING SHIFT
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
$\frac{144}{25}$
Open complete paper
15
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 20TH MAY EVENING SHIFT
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 $\frac{l_1{ }^2 l_2{ }^2}{100}=$
A
$\frac{20}{9}$
B
$\frac{16}{81}$
C
$\frac{4}{81}$
D
$\frac{2}{9}$
Open complete paper
16
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 20TH MAY EVENING SHIFT
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 $e^2=$
A
$\frac{\sqrt{7}}{2}$
B
$\frac{7}{2}$
C
$\frac{35}{4}$
D
$2 \sqrt{3}$
Open complete paper
17
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 20TH MAY MORNING SHIFT
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
A
2
B
$2 \sqrt{3}$
C
$2 / \sqrt{3}$
D
$\sqrt{3}$
Open complete paper
18
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 20TH MAY MORNING SHIFT
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
$y-x-1=0$
Open complete paper
19
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 21TH MAY EVENING SHIFT
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
Open complete paper
20
2024 · Mathematics · Coordinate Geometry · Hyperbola
AP EAPCET 2024 21TH MAY MORNING SHIFT
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
$4 x^2-9 y^2-24 x-36 y=0$
Open complete paper

Showing 20 of 55 questions