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Easy 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 y2=16xy^{2}=16 x then the slope of it is B: The parabola x2=pyx^{2}=p y passes through (12,16),(12,16), the focal distance of the point is C: If the parabola y2=kxy^{2}=k x passes through (9,6) then the value of kk is D: The Ordinate of the point on the parabola y2=36x\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
For hyperbola x2cos⁡2a−y2sin⁡2a=1\frac{x^{2}}{\cos ^{2} a}-\frac{y^{2}}{\sin ^{2} a}=1 which of the following remains constant with change in 'a'?
Q4MathsUnit 10: Co-ordinate Geometry
The sum of the focal distances of a point on the ellipse x24+y29=1\frac{x^{2}}{4}+\frac{y^{2}}{9}=1 is:
Q5MathsUnit 10: Co-ordinate Geometry
What is the vertical cross-section of a solid cylindrical pipe shown in the figure?
Q6MathsUnit 10: Co-ordinate Geometry
Triangle ABCA B C is inscribed in the parabola described by the equation y2−6x−4y+10=0y^{2}-6 x-4 y+10=0 so that AA is the vertex of the parabola and BB and CC are the end points of the latus rectum of the parabola. The area of triangle ABCA B C is

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