Question

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

Answer 1

curve, y² = 4x
differentiate with respect to x,
2y.dy/dx = 4
dy/dx = 2/y
Let (a,b) is the point on y² = 4y at which y = x + 1 is a tangent to it.
at, (a,b) dy/dx = 2/b = slope of tangent .
so, b² = 4a ------(1)

according to question,
equation of tangent is y = x + 1
slope of tangent = 1

so, 1 = 2/b => b = 2
put b = 2 in equation (1),
so, 2² = 4a => a = 1
hence, require point is (1,2)
therefore option (A) is correct.

Answer 2

Answer:

Step-by-step explanation:

Hope you understood.