Q42 / 92 · NTA Abhyas (JEE Main) 2020 · Mathematics · Parabola

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

A
$y = 2 x$
B
$y = 2 x - 3$
Correct answer
C
$y = 2 x + 3$
D
$y = 2 x + 5$

Solution

$y^{2} = 4 x + 5$ is same as $y^{2} = 4 (x + \frac{5}{4})$

The equation of the tangent to $y^{2} = 4 (x + \frac{5}{4})$ which is parallel to $y = 2 x + 7$ is

$y = 2 (x + \frac{5}{4}) + \frac{1}{2}$

$\Rightarrow y = 2 x + 3$

Hence, the correct answer is option: 'C'.

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

Solution

More Parabola Questions

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