Question

Find the equation to the straight line which passes through the point (x', y') and is perpendicular to the given straight line yy' = 2a (x + x').

Answer 1

The given straight line is

yy' - 2ax - 2ax' = 0.

Any straight line perpendicular to it is

2ay + xy' + C = 0 .........(1)

This will pass through the point (x', y') and therefore will be the straight line required if the coordinates x' and y' satisfy it,

Substituting in (1) for C the required equation is therefore

2a(y - y') + y'(x - x') = 0.