A straight line through a fixed point (2, 3) intersects the… — JEE Main 2018 Mathematics PYQ

JEE Main 2018

A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points

P

and

Q

. If

O

is the origin and the rectangle

OPRQ

is completed, then the locus of

R

A.
$3x + 2y = 6$
B.
$2x + 3y = xy$
C.
$3x + 2y = xy$
D.
$3x + 2y = 6xy$

Show answer and solution

Correct option: C

Solution

If P is on the x-axis at (a, 0) and Q is on the y-axis at (0, b), then R = (a, b) since OPRQ is a rectangle. The line PQ passes through (2, 3), so by intercept form: 2/a + 3/b = 1. Substituting a = x and b = y gives 2/x + 3/y = 1, which simplifies to 2y + 3x = xy, i.e., 3x + 2y = xy.

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JEE Main 2018 Mathematics question on Straight Lines and Pair of Lines