Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If a variable tangent of the circle x 2 + y 2 = 1 intersects the ellipse x 2 + 2y 2 = 4 at point P and Q, then the locus of the point of intersection of tangents at P and Q is:
A
A circle of radius 2 units
B
A parabola with focus as (2, 3)
C
An ellipse with eccentricity 
D
None of the above
Text Solution
Verified by ExpertsThe correct answer is:
C
Let point of intersection be (h, k). Then equation of the line passing through P and Q is hx + 2ky = 4 (chord of contact). Since hx + 2ky = 4 touches x 2 + y 2 = 1, 
i.e., 4k 2 + h 2 = 16. So required locus is 4y 2 + x 2 = 16, which is an ellipse of eccentricity 
and length of latus rectum is 2 units.
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