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  4. The equation of the tangent to the parabola y2=4x+5 which is parallel to the line y=2x+7 is

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

NTA AbhyasNTA Abhyas 2020Conic Sections

Solution:

$y^{2}=4x+5$ 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
$y=2\left(x + \frac{5}{4}\right)+\frac{1}{2}$
$\Rightarrow y=2x+3$