Parabola 1 Question 14

14. Let S be the focus of the parabola y2=8x and PQ be the common chord of the circle x2+y22x4y=0 and the given parabola. The area of PQS is

(2012)

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Solution:

  1. PLAN Parametric coordinates for y2=4ax are (at2,2at).

Description of Situation As the circle intersects the parabola at P and Q. Thus, points P and Q should satisfy circle.

P(2t2,4t) should lie on x2+y22x4y=04t4+16t24t216t=04t4+12t216t=04t(t3+3t4)=04t(t1)(t2+t+4)=0t=0,1

P(2,4) and PQ is the diameter of circle.

Thus, area of PQS=12OS×PQ=12(2)(4)=4



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