A tangent To The Circle x2 + y2 = 5 At The Point (–2, 1) Intersect The Ellipse at The Point A, B. If Tangents To The Ellipse At The Point A and B intersect At Point C. Find The Coordinate Of Points C.

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Question

A tangent to the circle x² + y²= 5 at the point (–2, 1) intersect the ellipse at the point A, B. If tangents to the ellipse at the point A and B intersect at point C. Find the coordinate of points C.

easy

Solution

Correct option is

Equation of tangent to the circle x² + y²= 5 at point (–2, 1) is

–2x + y – 5 = 0

2x – y + 5 = 0 … (1)

Let point C be (h, k)

Equation of line AB as a chord of contact from the point C with respect to ellipse

… (2)

As equation (1) and (2) respects same line

.

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