The line y = x + 1 is a tangent to the curve y² = 4x at the point
(A) (1, 2)   (B) (2, 1)   (C) (1, - 2)   (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.

For a curve y = f(x) containing the point (x₁,y₁) the equation of the tangent line to the curve at (x₁,y₁) is given by 

y − y₁ = f′(x₁) (x − x₁).

The equation of the given curve is y² = 4x

Differentiating with respect to x , we have:

2y dy/dx = 4

⇒ dy/dx = 2/y

The given line is y = x +1 which is of the form y = mx + c.

Hence, the slope of the line is 1

The line y = x +1 is a tangent to the given curve if the slope of the line is equal to the slope of the tangent.

Also, the line must intersect the curve.

Thus, we must have:

2 / y = 1

⇒ y = 2

Therefore,

y = x + 1

Substituting the value of y in the above equation, we get

⇒ x = y - 1

⇒ x = 2 - 1

⇒ x = 1

Hence, the line y = x + 1 is a tangent to the given curve at the point (1, 2).

Thus, the correct answer is A

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 27

The line y = x + 1 is a tangent to the curve y² = 4x at the point (A) (1, 2) (B) (2, 1) (C) (1, - 2) (D) (- 1, 2)

Summary:

The line y = x + 1 is a tangent to the curve y² = 4x at the point (1, 2). Thus, the correct answer is A