Question

A circle and a parabola y² = 4ax intersect at four points. The algebraic sum of the ordinates of the four points is

a. 0

b. 1

c. –1

d. 4

Answer 1

Correct option is a. 0

Let equation of circle be x² +y² +2gx+2fy+C = 0 and equation of parabola is x = at² , y = 2at

Solving it, we get

a² t⁴ +4a² t² +2agt² +4aft+c = 0

a²t⁴ +2a(2a + g)t² +4aft+c = 0

t₁ +t₂ +t₃ +t₄ = 0

Or 2at₁ +2at₂ +2at₃ +2at₄ = 0

y₁ +y₂ +y₃ +y₄ = 0