The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is
(A) 1  (B) 2  (C) 3  (D) 1/2

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

The equation of the tangent to the given curve is

y = mx + 1

Now, substituting y = mx + 1 in y² = 4x,

we get:

(mx + 1)² = 4x

⇒ m²x² + 1+ 2mx - 4x = 0

⇒ m²x² + (2m - 4)x + 1 = 0 ....(1)

Since a tangent touches the curve at one point,

the roots of equation (1) must be equal.

Therefore, we have:

Discriminant = 0

Here 'm' refers to the slope of the given line.

⇒ (2m - 4)² - 4(m²)(1) = 0

⇒ 4m² + 16 - 16m - 4m² = 0

⇒ 16 - 16m = 0

⇒ m = 1

Hence, the required value of m is 1.

Thus, the correct option is A

---

NCERT Solutions Class 12 Maths - Chapter 6 Exercise ME Question 21

The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is (A) 1 (B) 2 (C) 3 (D) 1/2

Summary:

The line y = mx + 1 is a tangent to the curve y² = 4x if the value of m is 1. Thus, the correct option is A