Question

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

Answer 1

We have y² = 4x
Substituting the value of  y = mx + 1 in y² = 4x, we get
(mx + 1)² = 4x
⇒ m²x² + 2mx + 1 = 4x
⇒ m²x² + (2m − 4)x + 1 = 0                       .....(1)
Since, a tangent touches the curve at a point, the roots of (1) must be equal.
∴ D = 0
⇒ (2m − 4)² − 4m² = 0
⇒ 4m² −16m + 16 − 4m² = 0
⇒ m = 1