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Previous year question hub

Parabola - Coordinate Geometry | Mathematics PYQ

Practice 29 previous year questions on Parabola (Coordinate Geometry) from AP EAPCET exams. Year-wise PYQ and mock test practice.

29Papers
5Years
29Questions
1Topics

Parabola question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 32 100%

Question type distribution

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

Multiple Choices 32 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
29 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
29 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Parabola
29 Qs

Paper coverage

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

AP EAPCET 2025 27TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2025 21ST MAY EVENING SHIFT
1 Qs
AP EAPCET 2025 21ST MAY MORNING SHIFT
1 Qs
AP EAPCET 2025 22ND MAY EVENING SHIFT
1 Qs
AP EAPCET 2025 22ND MAY MORNING SHIFT
1 Qs
AP EAPCET 2025 23RD MAY EVENING SHIFT
1 Qs
AP EAPCET 2025 23RD MAY MORNING SHIFT
1 Qs
AP EAPCET 2025 24TH MAY MORNING SHIFT
1 Qs
AP EAPCET 2025 26TH MAY EVENING SHIFT
1 Qs
AP EAPCET 2025 26TH MAY MORNING SHIFT
1 Qs
AP EAPCET 2024 18TH MAY MORNING SHIFT
2 Qs
AP EAPCET 2024 19TH MAY EVENING SHIFT
1 Qs
AP EAPCET 2024 20TH MAY MORNING SHIFT
1 Qs
AP EAPCET 2024 21TH MAY EVENING SHIFT
1 Qs
AP EAPCET 2024 22TH MAY EVENING SHIFT
1 Qs
AP EAPCET 2024 22TH MAY MORNING SHIFT
1 Qs
AP EAPCET 2024 23TH MAY MORNING SHIFT
1 Qs
AP EAPCET 2023 - 15th May Evening Shift
1 Qs
AP EAPCET 2023 - 15th May Evening Shift
1 Qs
AP EAPCET 2023 - 15th May Morning Shift
1 Qs
AP EAPCET 2023 - 15th May Morning Shift
1 Qs
AP EAPCET 2023 - 15th May Morning Shift
1 Qs
AP EAPCET 2022 4TH JULY MORNING SHIFT
2 Qs
AP EAPCET 2022 4TH JULY EVENING SHIFT
1 Qs
AP EAPCET 2022 5TH JULY MORNING SHIFT
1 Qs
AP EAPCET 2021 19TH AUGUST EVENING SHIFT
1 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 SHIFT20251View paper
AP EAPCET 2025 21ST MAY MORNING SHIFT20251View paper
AP EAPCET 2025 22ND MAY EVENING SHIFT20251View paper
AP EAPCET 2025 22ND MAY MORNING SHIFT20251View paper
AP EAPCET 2025 23RD MAY EVENING SHIFT20251View paper
AP EAPCET 2025 23RD MAY MORNING SHIFT20251View paper
AP EAPCET 2025 24TH MAY MORNING SHIFT20251View paper
AP EAPCET 2025 26TH MAY EVENING SHIFT20251View paper
AP EAPCET 2025 26TH MAY MORNING SHIFT20251View paper
AP EAPCET 2025 27TH MAY MORNING SHIFT20252View paper
AP EAPCET 2024 18TH MAY MORNING SHIFT20242View paper
AP EAPCET 2024 19TH MAY EVENING SHIFT20241View paper
AP EAPCET 2024 20TH MAY MORNING SHIFT20241View paper
AP EAPCET 2024 21TH MAY EVENING SHIFT20241View paper
AP EAPCET 2024 22TH MAY EVENING SHIFT20241View paper
AP EAPCET 2024 22TH MAY MORNING SHIFT20241View paper
AP EAPCET 2024 23TH MAY MORNING SHIFT20241View paper
AP EAPCET 2023 - 15th May Evening Shift20231View paper
AP EAPCET 2023 - 15th May Evening Shift20231View paper
AP EAPCET 2023 - 15th May Morning Shift20231View paper
AP EAPCET 2023 - 15th May Morning Shift20231View paper
AP EAPCET 2023 - 15th May Morning Shift20231View paper
AP EAPCET 2022 4TH JULY EVENING SHIFT20221View paper
AP EAPCET 2022 4TH JULY MORNING SHIFT20222View paper
AP EAPCET 2022 5TH JULY MORNING SHIFT20221View paper
AP EAPCET 2021 19TH AUGUST EVENING SHIFT20211View 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 Parabola previous year questions

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

1
2021 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2021 19TH AUGUST EVENING SHIFT

Find the equation of the parabola which passes through (6, \(-\)2), has its vertex at the origin and its axis along the Y-axis.

A
\(y^2=18x\)
B
\(x^2=18y\)
C
\(y^2=-18x\)
D
\(x^2=-18y\)
Open complete paper
2
2021 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2021 19TH AUGUST MORNING SHIFT

If one end of focal chord of the parabola \(y^2=8x\) is \(\left(\frac{1}{2},2\right)\), then the length of the focal chord is ................ units.

A
\(\frac{625}{4}\)
B
\(\frac{5}{\sqrt2}\)
C
\(\frac{25}{2}\)
D
25
Open complete paper
3
2021 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2021 20TH AUGUST EVENING SHIFT

The point of intersection of the latus rectum and axis of the parabola \(y^2+4 x+2 y-8=0\) is

A
\(\left(\frac{9}{4},-1\right)\)
B
\(\left(\frac{5}{4},-1\right)\)
C
\(\left(\frac{7}{2}, \frac{5}{2}\right)\)
D
\(\left(\frac{-5}{4}, 1\right)\)
Open complete paper
4
2021 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2021 20TH AUGUST MORNING SHIFT

The coordinates of the focus of the parabola described parametrically by \(x=5t^2+2\) and \(y=10t+4\) (where t is a parameter) are

A
(7, 4)
B
(3, 4)
C
(3, \(-\)4)
D
(\(-\)7, 4)
Open complete paper
5
2022 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2022 4TH JULY EVENING SHIFT

Suppose a parabola passes through \((0,4),(1,9)\) and \((4,5)\) and has its axis parallel to the \(Y\)-axis. Then, the equation of the parabola is

A
\(19 x^2+12 y-79 x-48=0\)
B
\(19 x^2+12 y-79 x+48=0\)
C
\(19 y^2+12 x-79 y-48=0\)
D
\(19 y^2+12 x-79 y+48=0\)
Open complete paper
6
2022 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2022 4TH JULY MORNING SHIFT

Suppose a parabola with focus at \((0,0)\) has \(x-y+1=0\) as its tangent at the vertex. Then, the equation of its directrix is

A
\(x-y+2=0\)
B
\(x-y-2=0\)
C
\(x-y+3=0\)
D
\(x-y+4=0\)
Open complete paper
7
2022 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2022 4TH JULY MORNING SHIFT

If \(a x+b y=1\) is a normal to the parabola \(y^2=4 p x\), then the condition is

A
\(4 a b=a^2+b^2\)
B
\(4 p a b+a b^3=a^2 b^2\)
C
\(p a^3=b^2-2 p a b^2\)
D
\(p a^2+4 p a=a+b\)
Open complete paper
8
2022 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2022 5TH JULY MORNING SHIFT

Which of the following represents a parabola?

A
\(x=4 \cos t, y=4 \sin t\)
B
\(x^2-2=-2 \cos t, y=\cos ^2\left(\frac{t}{2}\right)\)
C
\(\sqrt{x}=\tan t, \sqrt{y}=\sec t\)
D
\(x=\sqrt{1-\sin t}, y=\sin \left(\frac{t}{2}\right)+\cos \left(\frac{t}{2}\right)\)
Open complete paper
9
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 18TH MAY MORNING SHIFT
If the axes are rotated through an angle $45^{\circ}$ about the origin in anticlockwise direction, then the transformed equation of $y^2=4 a r$ is
A
$(x+y)^2=4 \sqrt{2} a(x-y)$
B
$(x-y)^2=4 \sqrt{2} a(x+y)$
C
$(x-y)^2=\frac{43}{\sqrt{2}}(x-y)$
D
$(x+y)^2=\frac{4 a}{\sqrt{2}}(x-y)$
Open complete paper
10
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 18TH MAY MORNING SHIFT
The line $x-2 y-3=0$ cuts the parabola $y^2=4 \operatorname{ar}$ at the points $P$ and $Q$. If the focus of this parabola is $\left(\frac{1}{4}, k\right)$. then $P Q=$
A
$16 a \sqrt{5}$
B
$8 a \sqrt{5}$
C
$4 a \sqrt{5}$
D
$2 a \sqrt{5}$
Open complete paper
11
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 19TH MAY EVENING SHIFT
The normal drawn at a point $(2,-4)$ on the parabola $y^2 \pm 8 x$ cuts again the same parabola at $(\alpha, \beta)$, then $\alpha+\beta=$
A
8
B
16
C
24
D
30
Open complete paper
12
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 20TH MAY MORNING SHIFT
A common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8 x$ is
A
$3 x-\sqrt{3 y}+2=0$
B
$x-\sqrt{3} y+6=0$
C
$2 x-\sqrt{3} y+3=0$
D
$x-3 y+6=0$
Open complete paper
13
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 21TH MAY EVENING SHIFT
If the ordinates of points $P$ and $Q$ on the parabola $y^2=12 x$ are in the ratio $1: 2$. Then, the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is
A
$y+18\left(\frac{x-6}{21}\right)^{\frac{3}{2}}=0$
B
$y-18\left(\frac{x-6}{12}\right)^{\frac{3}{2}}=0$
C
$y+12\left(\frac{x-6}{14}\right)^{\frac{1}{2}}=0$
D
$y-12\left(\frac{x-6}{18}\right)^{\frac{1}{2}}=0$
Open complete paper
14
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 22TH MAY EVENING SHIFT
Equation of the line touching both parabolas $y^2=4 x$ and $x^2=-32 y$ is
A
$x+2 y+4=0$
B
$2 x+y-4=0$
C
$x-2 y-4=0$
D
$x-2 y+4=0$
Open complete paper
15
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 22TH MAY MORNING SHIFT
If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex, then $\theta=$
A
$45^{\circ}$
B
$90^{\circ}$
C
$135^{\circ}$
D
$60^{\circ}$
Open complete paper
16
2024 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2024 23TH MAY MORNING SHIFT

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12 x$ and a point on the parabola in the ratio $1: 2$. Then, the locus of $p$ is

A
$y^2=2(x-2)$
B
$y^2=4 x$
C
$y^2=4(x-2)$
D
$y^2=9(x-3)$
Open complete paper
17
2025 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2025 21ST MAY MORNING SHIFT

If $L$ is the normal drawn to the parabola $y^2=8 x$ at the point $t=\frac{1}{\sqrt{2}}$, then the foot of the perpendicular drawn from the focus of the parabola on to the normal $L$ is

A

$(3,2)$

B

$(5, \sqrt{2})$

C

$(0, \sqrt{2})$

D

$(3, \sqrt{2})$

Open complete paper
18
2025 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2025 21ST MAY EVENING SHIFT

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4 x$ is

A

$\frac{\pi}{6}$

B

$\frac{\pi}{4}$

C

$\frac{\pi}{3}$

D

$\frac{\pi}{2}$

Open complete paper
19
2025 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2025 22ND MAY EVENING SHIFT

If the perpendicular distance from the focus of a parabola $y^2=4 a x$ to its directrix is $\frac{3}{2}$, then the equation of the normal drawn at $(4 a,-4 a)$ is

A

$2 x+y=3$

B

$2 x-y=9$

C

$x-2 y=9$

D

$x+2 y+3=0$

Open complete paper
20
2025 · Mathematics · Coordinate Geometry · Parabola
AP EAPCET 2025 22ND MAY MORNING SHIFT

$P Q$ is a focal chord of the parabola $y^2=4 x$ with focus $S$. If $P=(4,4)$, then $S Q=$

A

2

B

$\frac{5}{4}$

C

5

D

$\frac{3}{2}$

Open complete paper

Showing 20 of 29 questions