Verified Solution • 2025–26 Session moderate

QJEEM21Ma7dbc: JEE Main 2021 Mathematics - Class 11 JEEM21Ma7dbc Solution: Let A(1, 4) and B(1, 5) be two points. Let P be a point on the…

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 :

Multiple Choice Options

  • A a straight line
  • B an ellipse
  • C a parabola
  • D a hyperbola

Step-by-Step Verified Solution

P be a point on (x−1)2+(y−1)2=1{(x - 1)^2} + {(y - 1)^2} = 1

so P(1+cos⁡θ,1+sin⁡θ)P(1 + \cos \theta ,1 + \sin \theta )

A(1, 4), B(1, −- 5)

(PA)2+(PB)2{(PA)^2} + {(PB)^2}

=(cos⁡θ)2+(sin⁡θ−3)2+(cos⁡θ)2+(sin⁡θ+6)2= {(\cos \theta )^2} + {(\sin \theta - 3)^2} + {(\cos \theta )^2} + {(\sin \theta + 6)^2}

=47+6sin⁡θ= 47 + 6\sin \theta

It is maximum if sin⁡θ=1\sin \theta = 1

When sin⁡θ=1,cos⁡θ=0\sin \theta = 1,\cos \theta = 0

So P(1, 2), A(1, 4), B(1, −- 5)

P, A, B are collinear points.

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