JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Parabola

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 ?

(A) $(5, 4)$ ✓ Correct
(B) $(- 6, 0)$
(C) $(0, 3)$
(D) $(4, 5)$

Answer: (A)

Solution

The line

2 x + y = 1

has slope

- 2

, so a perpendicular tangent has slope

\frac{1}{2}

. For the parabola

y^{2} = 6 x

, the equation of a tangent with slope

m

y = m x + \frac{3}{2 m}

. With

m = \frac{1}{2}

y = \frac{x}{2} + 3

, or

x - 2 y + 6 = 0

. Check each point: (A)

(5, 4)

5 - 8 + 6 = 3 \neq = 0

(does NOT lie). (B)

(- 6, 0)

- 6 - 0 + 6 = 0

(lies). (C)

(0, 3)

0 - 6 + 6 = 0

(lies). (D)

(4, 5)

4 - 10 + 6 = 0

(lies). So

(5, 4)

does NOT lie on the tangent.

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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