NIMCET 2007 — Mathematics PYQ

Using General Perpendicular Form

The general equation of any line perpendicular to $ax+by+c=0$ is written as:

$$bx-ay+\lambda =0$$

Given line equation:

$$2x-3y+6=0$$

Here, $a=2$ and $b=-3$. Therefore, the equation of a line perpendicular to it will be:

$$-3x-2y+\lambda =0$$

Multiplying the entire equation by $-1$ to make it look like the standard options:

$$3x+2y+k=0$$

(where $k=-\lambda$)

Since this line passes through the point $(-2,3)$, substitute $x=-2$ and $y=3$ into the equation to find $k$:

$$3(-2)+2(3)+k=0$$

$$-6+6+k=0$$

$$k=0$$

Substituting $k=0$ back into our equation:

$$3x+2y=0$$