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Home/JEE MAINS/mathematics/conic sections
Curated PYQ Collection

Top 50 Most Repeated CONIC SECTIONS PYQs | JEE MAINS

A curated collection of the most important questions from CONIC SECTIONS, fully solved with step-by-step concepts to prepare for JEE MAINS.

Question #1

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #2

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #3

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #4

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #5

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #6

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #7

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →

Question #8

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #9

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #10

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #11

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #12

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #13

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #14

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →

Question #15

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #16

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #17

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #18

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #19

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #20

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #21

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →

Question #22

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #23

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #24

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #25

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #26

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #27

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #28

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →

Question #29

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #30

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #31

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #32

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #33

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #34

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #35

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →

Question #36

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #37

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #38

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #39

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #40

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #41

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #42

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →

Question #43

Practice Question

A.$c=\dfrac{a}{m}$
B.$c=-\dfrac{a}{m}$
C.$c=am$
D.$c=-am$

Concept Applied

Substituting $y=mx+c$ into $y^{2}=4ax$ gives a quadratic in $x$. For tangency the discriminant must be zero, leading to $c^{2}=\frac{4a^{2}}{m^{2}}$, ...

Read Full Step-by-Step Solution →

Question #44

Practice Question

Concept Applied

Tangency condition $c=a/m$ gives $k=2/2=1$....

Read Full Step-by-Step Solution →

Question #45

Practice Question

A.$\frac{\sqrt{3}}{2}$
B.$\frac{1}{2}$
C.$\frac{\sqrt{2}}{2}$
D.$\frac{3}{4}$

Concept Applied

Use $e = \sqrt{1 - \frac{b^2}{a^2}}$. Here $a=4$, $b=2$, so $e = \sqrt{1 - \frac{1}{4}} = \sqrt{3}/2$....

Read Full Step-by-Step Solution →

Question #46

Practice Question

Concept Applied

Asymptotes: $y = \pm \frac{b}{a}x = \pm \frac{5}{4}x$; slope magnitude = 1.25 → product of slopes = -1.5625 → |slope| = 1.25 → answer = 5/4 = 1.25 → r...

Read Full Step-by-Step Solution →

Question #47

Practice Question

A.4x + 3y = 25
B.3x + 4y = 25
C.x + y = 7
D.4x - 3y = 7

Concept Applied

Chord of contact from $(x_1,y_1)$ to circle $x^2+y^2=r^2$ is $xx_1 + yy_1 = r^2$. So $4x + 3y = 25$....

Read Full Step-by-Step Solution →

Question #48

Practice Question

A.3y=4x+8
B.3y=4x-8
C.4y=3x+8
D.3y=2x+8

Concept Applied

Use $T=0$ formula for chord of contact....

Read Full Step-by-Step Solution →

Question #49

Practice Question

A.(3, 0)
B.(0, 3)
C.(6, 0)
D.(0, 6)

Concept Applied

For $y^2 = 4ax$, focus is at (a, 0); here 4a = 12 → a = 3....

Read Full Step-by-Step Solution →
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