1)

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


A) 5

B) 4

C) 3

D) 2

Answer:

Option B

Explanation:

Concept Involved Parametric coordinates for y2=4ax are(at2,2at).

23112021868_u1.PNG

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

Sol. p(2t2,4t) sholud lie on

 x2+y22x4y=0

   4t4+16t24t216T0

   4t4+12t216t=0

  4t(t3+3t4)=0

   4t(t1)(t2+t+4)=0

   t=0,1P(2,4)

 Thus, are of OPs=12OS×PQ

2311202171_u2.PNG