Question

If the line y = mx + 1 is tangent to the parabola y² = 4x then find the value of m.

Answer 1

Given that y² = 4x   ......(i)

And y = mx + 1   .....(ii)

From equation (i) and (ii) we get

(mx + 1)² = 4x

⇒ m²x² + 1 + 2mx – 4x = 0

⇒ m²x² + (2m – 4)x + 1 = 0

Applying condition of tangency, we have

(2m – 4)² – 4m² × 1 = 0

⇒ 4m² + 16 – 16m – 4m² = 0

⇒ – 16m = – 16

⇒ m = 1

Hence, the required value of m is 1.