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 Correct Option is A

The equation of the given curve is y²=4x.

Differentiating with respect to x, we have:

2y \(\frac{dy}{dx}\)=4=\(\frac{dy}{dx}\)=2y

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

\(\frac{dy}{dx}\)=\(\frac{2}{y}\)

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

∴ The slope of the line = 1 The line y = x + 1 is 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:

\(\frac{2}{y}\)=1

y=2

Now, y=x+1=x=y-1=x=2-1=1

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

The correct answer is A.