Question

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)

Answer 1

The equation of the given curve is . y²=4x
Differentiating with respect to x, we have:

Therefore, the slope of the tangent to the given curve at any point (x, y) is given by,

The given line is y = x + 1 (which is of the form y = mx + c)
∴ Slope of the line = 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:

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