IIT-JEE 1984Question 1
Two equal sides of an isosceles triangle are given by the equations $7x-y+3=0$ and $x+y-3=0$ and its third side passes through the point $(1,-10)$. Determine the equation of the third side.
Points and Straight Lines
Answer$x-3y-31=0$ or $3x+y+7=0$
Solution
Third line through $(1,-10)$ with slope $m$ makes equal angles with slopes $7$ and $-1$: $\frac{m-7}{1+7m}=\pm\frac{m+1}{1-m}$ gives $m=\frac13$ or $m=-3$. Lines: $x-3y-31=0$ or $3x+y+7=0$.