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

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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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