NIMCET 2023 — Mathematics PYQ

1. Point Coordinates:

A point in the fourth quadrant that is equidistant from the axes is of the form $(h,-h)$, where h > 0.

Let the point of intersection be $(h,-h)$.

2. Substitution in Line Equations:

Since this point lies on both lines, it must satisfy both equations:

For the first line:

$4a(h)+2a(-h)+c=0$

$4ah-2ah+c=0$

$2ah+c=0$

$h=\frac{-c}{2a}$ ...(i)

For the second line:

$5b(h)+2b(-h)+d=0$

$5bh-2bh+d=0$

$3bh+d=0$

$h=\frac{-d}{3b}$ ...(ii)

3. Equating the values of $h$:

From equations (i) and (ii):

4. Cross-multiplication:

Correct Option: 3