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JEE 2020 Mathematics : Conic Section - 02 (09.09.2019)

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Question 1

The locus of the foot of perpendicular drawn from the centre of the ellipse x² + 3y² = 6 on any tangent to it is

Question 2

The area (in sq. units) of the quadrilateral formed by the tangents at the points of the latera recta to the ellipse

= 1, is

Question 3

The tangent is drawn at (a cos θ, b sin θ) on the ellipse b²x² + a²y² – a²b² = 0. It meets the auxiliary circle of the ellipse in two points. If the angle subtended by the chord joining two points at the centre of ellipse is π/2, then the eccentricity of the ellipse is

Question 4

The locus of the middle points of the portion of the tangents of the ellipse $Description: Description: D:\GradeStack Courses\JEE Mains (Sent by Ravi)\JEE Mains Full Test\AIEEE-Full-Test-4-New_files\image339.png$ included between the axis is the curve

Question 5

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity is

Question 6

The ellipse x² + 4y² = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

Question 7

The set of values of ‘a’ for which (13x – 1)² + (13y – 2)² = a (5x + 12y – 1)² represents an ellipse, is-

Question 8

What is the distance between the foci and the ends of the minor axis of the given ellipse -

+ = 1?

Question 9

If S and S′ are foci and A be one end of minor axis of ellipse

= 1, then area of ΔSAS′is-

Question 10

The eccentricity of an ellipse whose centre is at the origin is 1/2, If one of its directrix is x=−4, then the equation of the normal to it at (1, 3/2) is:

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