Question

A line passes through $A(-3,0)$ and $B(0,-4)$. A variable line perpendicular to $AB$ is drawn to cut $x$ and $y-$axes at $M$ and $N$. Find the locus of the point of intersection of the lines $AN$ and $BM$.

Answer 1

The line perpendicular to AB would be 3x - 4y = K, so M would be (K/3,0) and N would be (0,-K/4)
Eq. of AN would be (y-0) = -K/12 (x+3) and eq. of (y+4) = 12/K (x-0)
Kx+12y + 3K = 0 and 12x - Ky - 4K = 0, find the point of intersection and equate the x coordinate to X and x coordinate to Y. Eliminate K and get the locus