Question

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

Answer 1

Solving the given equations,

y = mx + 1 & y² = 4x

(mx + 1)² = 4x

m²x² + 2mx + 1 = 4x

m²x² + 2mx – 4x + 1 = 0

m+x² + x (2m – 4) + 1 = 0

As the line touches the parabola, above equation must have equal roots,

Discriminant (D) = 0

(2m – 4)² - 4 (m²) (1) = 0

4m² - 16m + 16 – 4m² = 0

-16 m + 16 = 0

- m + 1 = 0

m = 1

Hence, the required value of m is 1.