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

Answers (1)

The slope of the given line y = x+1 is 1
given curve equation is
y^2 = 4 x 
If the line is tangent to the given curve than the slope of the tangent is equal to the slope of the curve
The slope of tangent = 2y\frac{dy}{dx} = 4 \Rightarrow \frac{dy}{dx} = \frac{2}{y}
\frac{dy}{dx} = \frac{2}{y} = 1\\ y = 2
Now, when y = 2, x = \frac{y^2}{4} = \frac{2^2}{4} = \frac{4}{4} = 1
Hence, the coordinates are (1,2)

Hence, (A) is the correct answer

 

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