Let P(1, 2) be a point from which pair of tangents are drawn to the ellipse \frac{x^{2}}{4} + y^{2} = 1 . Tangents touch the ellipse at points A and B. If the point of intersection of normals at points A and B is Q, then equation of PQ is

Engineering

Mathematics

Chord of Contact in Ellipse

Question

Let P(1, 2) be a point from which pair of tangents are drawn to the ellipse $\frac{x^{2}}{4} + y^{2} = 1$ . Tangents touch the ellipse at points A and B. If the point of intersection of normals at points A and B is Q, then equation of PQ is

2x + y = 4

3x – 2y + 1 = 0

2x – y = 0

3x + 2y = 7

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Point P lies on the director circle

⇒ P, Q and the centre of the ellipse are collinear.

⇒ equation of PQ is 2x – y = 0