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asked in JEE by (154 points)

x2+ y2 -2x-4y-20=0 . If C be the centre of the circle , then the area of the quadrilateral PQCR is:

  • 450 sq. unit
  • 15 sq. unit
  • 50 sq. unit
  • 75 sq. unit
  • 175 sq. unit

1 Answer

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Given that the equation of the circle

x2+y2-2x-4y-20=0

=>(x-1)2+(y-2)2=20+12+22=52

The coordinates of the center C of the circle = (1,2)

So radius of the circle r= 5 unit = CR=CQ

Given the coordinates of external point P  = (16,7)we get

PC2 =[(16-1)2+(7-2)2]=250

So PR2=PQ2= PC2 -r2= 250-52=225

Hence PR=PQ= 15

Area of  PCQ and PCR= 1/2 *15*5 sq unit

Hence area of PQCR = 75 sq unit

 

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