Question

A line through A(−5, −4) meets the lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x − y − 5 = 0 at the points B, C and D, respectively. If

(15/AB)² + (10/AC)² = (6/AD)²  then find the equation of line.

Answer 1

Let the line through A(−5, −4) be

Therefore, every point on the line is of the form x

Similarly, points C and D lie on 2x + y + 4 = 0 and x − y − 5 = 0, respectively. We have

Hence, the equation of the line is