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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)
Asked by Yadagiri Last Modified
Answer 
Tasneem
The equation of the given curve is
.
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.
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