JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Straight Lines

A line passing through the point

A (9, 0)

makes an angle of

3 0^{\circ}

with the positive direction of x-axis. If this line is rotated about A through an angle of

1 5^{\circ}

in the clockwise direction, then its equation in the new position is

(A) $\frac{y}{3 - 2} + x = 9$ ✓ Correct
(B) $\frac{x}{3 - 2} + y = 9$
(C) $\frac{x}{3 + 2} + y = 9$
(D) $\frac{y}{3 + 2} + x = 9$

Answer: (A)

Solution

The line initially makes

3 0^{\circ}

with the x-axis; rotating it

1 5^{\circ}

clockwise about

A (9, 0)

gives a new inclination of

1 5^{\circ}

, so slope

= tan 1 5^{\circ} = 2 - 3

.

Equation:

y = (2 - 3) (x - 9)

, i.e.

\frac{y}{2 - 3} = x - 9

.

Since

\frac{1}{2 - 3} = 2 + 3 = - \frac{1}{3 - 2}

, this is equivalent to

\frac{y}{3 - 2} + x = 9

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Single correct option

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