The Tangent And The Normal To The Ellipse x2 + 4y2 = 4 At A Point P on It Meet The Major Axis In Q and R respectively. If QR = 2, Then The Eccentric Angle Of P is

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Question

The tangent and the normal to the ellipse x² + 4y² = 4 at a point P on it meet the major axis in Q and R respectively. If QR = 2, then the eccentric angle of P is

None of these

medium

Solution

Correct option is

x² + y² = 4 a² = 4, b² = 1

Let θ be eccentric angle at any point P of ellipse,

Tangent at

Normal at

Putting values of a and b; tangent is

… (1)

and normal as … (2)

Major axis is y = 0 … (3)

(1) and (2) meet major at Q and R

given

Solve to get

.

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