Mathematics · JEE

Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms Concepts for JEE

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Master Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms is a core JEE Main Mathematics subtopic under Co-ordinate Geometry. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms in the JEE syllabus
Memorise key formulas and standard results linked to Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms and reattempt after 48 hours

Common trap

Students often rush Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Co-ordinate Geometry in JEE Main Mathematics.

Free sample questions

Attempt 8 free MCQs for Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms. Unlock 1+ more with Pro.

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Q1MathsUnit 10: Co-ordinate Geometry

Arrange in the descending order of the values: A: If (9,12) is one end of a focal chord of the parabola

y^{2}=16 x

then the slope of it is B: The parabola

x^{2}=p y

passes through

(12,16),

the focal distance of the point is C: If the parabola

y^{2}=k x

passes through (9,6) then the value of

k

is D: The Ordinate of the point on the parabola

\boldsymbol{y}^{2}=\mathbf{3 6 x}

whose ordinate is three times its abscissa is Write the value of the above statements in the descending order

Q2MathsUnit 10: Co-ordinate Geometry

if the distance between the foci is equal to the length of the latus-rectum. Find the eccentricity of the ellipse.

Q3MathsUnit 10: Co-ordinate Geometry

Assertion The equation

3 x^{2}-2 y^{2}+4 x-6 y=0

represents a hyperbola. Reason The second degree equation

a x^{2}+

2 h x y+b y^{2}+2 g x+2 f y+c=0

represents a hyperbola if

a b c+2 f g h-

\boldsymbol{a} \boldsymbol{f}^{2}-\boldsymbol{b} \boldsymbol{g}^{2}-\boldsymbol{c h}^{2} \neq \boldsymbol{0} \& \boldsymbol{h}^{2}>\boldsymbol{a b}

Q4MathsUnit 10: Co-ordinate Geometry

For hyperbola

\frac{x^{2}}{\cos ^{2} a}-\frac{y^{2}}{\sin ^{2} a}=1

which of the following remains constant with change in 'a'?

Q5MathsUnit 10: Co-ordinate Geometry

A

and

B

are fixed points. If

|P A-P B|

is a constant, locus of

\boldsymbol{P}

Q6MathsUnit 10: Co-ordinate Geometry

The sum of the focal distances of a point on the ellipse

\frac{x^{2}}{4}+\frac{y^{2}}{9}=1

is:

Q7MathsUnit 10: Co-ordinate Geometry

What is the vertical cross-section of a solid cylindrical pipe shown in the figure?

Q8MathsUnit 10: Co-ordinate Geometry

Triangle

A B C

is inscribed in the parabola described by the equation

y^{2}-6 x-4 y+10=0

so that

A

is the vertex of the parabola and

B

and

C

are the end points of the latus rectum of the parabola. The area of triangle

A B C

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Frequently asked questions

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Focus on core ideas across Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms. JEE tests application, not just memorisation.