Question

The equation of the tangent to the parabola $y^2=4x+5$ which is parallel to the line $y=2x+7$ is

• A. $y=2x$
• B. $y=2x-3$
• C. $y=2x+3$
• D. $y=2x+5$

Answer 1

Answer: (C)

$y^2=4x+5$ is same as $y^2=4\left(x+\frac{5}{4}\right)$
The equation of the tangent to $y^2=4\left(x+\frac{5}{4}\right)$ which is parallel to $y=2x+7$ is
$y=2\left(x+\frac{5}{4}\right)+\frac{1}{2}$
$\Rightarrow y=2x+3$