A tangent is drawn to the parabola $y^{2} = 6 x$ which is perpendicular to the line $2 x + y = 1$ . Which of the following points does $NOT$ lie on it ?

(0, 3)

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(- 6, 0)

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(4, 5)

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(5, 4)

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Solution

The correct option is D $(5, 4)$
For $y^{2} = 6 x, a = \frac{3}{2}$
equation of tangent $: y = m x + c$
$\Rightarrow y = m x + \frac{3}{2 m}$
$∵ c = \frac{a}{m}$
and
$m = \frac{1}{2} (∵$ perpendicular to line $2 x + y = 1)$
$∴$ tangent is : $y = \frac{x}{2} + \frac{3}{1} \Rightarrow x - 2 y + 6 = 0$

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Similar questions

y^{2} = 6 x

2 x + y = 1

NOT

y = x + 2

y^{2} = 8 x

y^{2} = 8 x

y = x + 2.

The coordinates of the point of contact of the tangent to the parabola $y^{2} = 16 x$ , which is perpendicular to the line $2 x - y + 5 = 0$ are

\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1

(8, 3 \sqrt{3})

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