Question

If a circle and a parabola intersect in 4 points then the algebraic sum of the ordinates is

• A. Proportional to the arithmetic mean of the radius and the latus rectum
• B. Equal to zero
• C. Equal to the ratio of the arithmetic mean and the latus-rectum
• D. None of these

Answer 1

Answer: (B)

Equal to zero

Answer 2

Let the equations of the circle and that of the parabola be
x²+ y² + 2gx + 2fy + c = 0 and y² = 4ax respectively.

Eliminating x from these equation, we get

y⁴ + y²(16a² + 8ag) + 32a² fy + 16a²c = 0

⇒ y₁ + y₂ + y₃ + y₄ = 0.