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P, Q, and R are the feet of the norma...

P, Q, and R are the feet of the normals drawn to a parabola ( `y−3 ) ^2 =8( x−2 )` . A circle cuts the above parabola at points P, Q, R, and S . Then this circle always passes through the point.     (a)   (  2, 3   )           (b)      (        3, 2   )            (c)      (        0, 3   )       (d)      (        2, 0   )

A

(2,3)

B

(3,2)

C

(0,3)

D

(2,0)

Text Solution

Verified by Experts

(1) A circle through three co-normal point of a parabola always passes through the vertex of the parabola. Hence, the circle through P,Q,R and S out of which P,Q and R are co-normals points will always pass through vertex (2,3) of the parabola.
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