Question

The line y = mx + 1 is a tangent to the curve y^ 2 = 4x if the value of m is (A) 1 (B) 2 (C) 3 (D)1/2

Answer 1

given, equation of the tangent to the given curve is
y = mx + 1
Now, substituting the value of y in y² = 4x, we get
⇒ (mx + 1)² = 4x
⇒ m²x² + 1 + 2mx - 4x =0
⇒ m²x² + x(2m - 4) + 1 =0----------(1)
Since, a tangent touches the curve at one point, the root of equation (1) must be equal.
Thus, we get
Discriminant,D = b²- 4ac = 0
(2m - 4)² – 4(m²)(1) = 0 [ see equation (1)]
⇒ 4m² -16m + 16 - 4m² =0
⇒ -16m + 16 = 0
⇒ m =1
hence, the required value of m is 1.
therefore, option (A) is correct.