Given equation of ellipse and circle are 9x2+4y2=1 and x2+y2=9.
⇒P≡(3cosθ,2sinθ)andQ≡(3cosθ,3sinθ)
Let, R≡(h,k)
⇒h=3cosθ,k=718sinθ
⇒3h=cosθ,187k=sinθ
So, locus of R is given by, 9x2+32449y2=1.
⇒e=1−49×9324
⇒e=21117
⇒e=713
Let P be a point on the ellipse 9x2+4y2=1. Let the line passing through P and parallel to y−axis meet the circle x2+y2=9 at point Q such that PandQ are on the same side of the x−axis. Then, the eccentricity of the locus of the point R on PQ such that PR:RQ=4:3 as P moves on the ellipse, is:
Held on 1 Feb 2024 · Verified 6 Jul 2026.
1911
2113
23139
713
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