Question bank/JEE Main/Mathematics

Let P and Q be any two points on the lines represented by 2x -3y
= 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O
is origin) is 5, then the equation of the locus of mid-point of PQ, is
$ax^{2} + by^{2} + c = 0$, then the value of [IMAGE].

A2B4C6D8

Show answer and solution▾

Let point on line 2x - 3y = 0 be [IMAGE] and
point Q on line 2x + 3y = 0 [IMAGE] Area of triangle OPQ [IMAGE]....(1)
Coordinates of midpoint of PQ
$x = \frac{h + k}{2} \Rightarrow 2x = h + k$...(2)
$y = \frac{\frac{2h}{3} - \frac{2k}{3}}{2} = \frac{h - k}{3}$
$\Rightarrow 2y = h - k$...(3)
By (1),(2) and (3) required locus
$\Rightarrow 4x^{2} - 5y^{2} + 30 = 0$ or $4x^{2} - 9y^{2} - 30 = 0$

Source: Grass-G / M-11 Mathematics Paper-2 1Nov.docx