Question

TP and TQ are tangents to parabola y² = 8x and normals at P and Q intersect at a point R on the parabola. The locus of circumcentre of ΔTPQ is a parabola whose -

(A)  Vertex is (2, 0)

(B) foot of perpendicular from focus on the directrix is (7/4 , 0)

(C)  length of latus rectum is 1

(D) focus is (9/4, 0)

Answer 1

Correct option  (A)(B)(C)(D)

Explanation:

t₁ t₂ = 2 and t₁ + t₂ + t₃ = 0 and a = 2

∴ Let circumcentre of  Let circumcentre of  ΔTPQ be O(h,k) O(h, k) will be mid point of RT