If a point P 0 , - 2 and Q is any point on the circle, x 2 + y 2 - 5 x - y + 5 = 0 , then the maximum value…

If a point P0,-2 and Q is any point on the circle, x2+y2-5x-y+5=0, then the maximum value of PQ2 is
  1. 8+53
  2. 47+1062
  3. 14+53
  4. 25+ 62

Solution

Given circle x2+y2-5x-y+5=0
⇒x-522+y-122=32
On circle Q=(52+32cosθ,12+32sinθ)

PQ2=52+32cos⁡θ​2+52+32sin⁡θ​2

PQ2=252+32+532cosθ​+sinθ​

=14+532cos⁡θ​+sin⁡θ​

∴Maximum value of PQ2=14+5322

=14+53.

Asked in: JEE Main 2017 (08 Apr Online)

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