Mathematics · JEE

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

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The most important Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms questions for JEE cover conceptual traps, standard results, and numerical patterns from Sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms. Goodmarks provides 9+ high-yield MCQs with full solutions.

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Syllabus context

Part of Co-ordinate Geometry in JEE Main Mathematics.

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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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