P be a point on (x−1)2+(y−1)2=1, so P(1+cosθ,1+sinθ).
Given A(1,4)&B(1,-5)
(PA)2+(PB)2
=(cosθ)2+(sinθ−3)2+(cosθ)2+(sinθ+6)2
=47+6sinθ is maximum if sinθ=1
⇒sinθ=1,cosθ=0
P(1,2),A(1,4),B(1,−5)
The points P,A and B lie on the line x=1.
JEE Main 2021 — Mathematics Coordinate Geometry
Let A(1,4) and B(1,−5) be two points. Let P be a point on the circle ((x−1))2+(y−1)2=1, such that (PA)2+(PB)2 have maximum value, then the points, P,A and B lie on
Held on 26 Feb 2021 · Verified 6 Jul 2026.
a hyperbola
a straight line
an ellipse
a parabola
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