JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Parabola

Axis of a parabola lies along

x

- axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive

x

- axis then which of the following points does not lie on it?

(A) $(5, 26)$
(B) $(8, 6)$ ✓ Correct
(C) $(6, 42)$
(D) $(4, - 4)$

Answer: (B)

Solution

The vertex at

(2, 0)

and focus at

(4, 0)

give

a = 2

, so the parabola is

y^{2} = 8 (x - 2)

, which parametrises as

(2 + 2 t^{2}, 4 t)

. Testing the points:

(5, 26)

needs

t^{2} = \frac{3}{2}

and gives

y = 26

, which fits;

(6, 42)

needs

t^{2} = 2

giving

y = 42

, fits;

(4, - 4)

needs

t^{2} = 1

giving

y = \pm 4

, fits. But

(8, 6)

needs

t^{2} = 3

, which forces

y = \pm 43 \neq = 6

, so that point does not lie on the parabola.

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

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