Question

Prove that a straight line and parabola cannot intersect at more than two points

Answer 1

Let the standard equation of parabola y² = 4ax ......(1)

Equation of line be y = mx + c  ......(2)

Solving (1) and (2)

(mx + c)² = 4ax

⇒ mx² + 2mcx + c² – 4ax = 0

⇒ mx² + 2x(mc – 2a) + c² = 0

This equation cannot have more than two solutions

And

Hence a line and parabola cannot intersect at more than two points.