Question

find the equation of the straight line passing through the point (a,b),(a+b,a-b)

Answer 1

Given ,

The straight line passing through the point (a,b) and (a+b,a-b)

We know that , the two point form is given by

$\boxed{ \sf{y - y_{1} = \frac{ y_{2} -y_{1} }{x_{2} - x_{1}} (x - x_{1})}}$

Thus ,

$\sf \mapsto y - b =( \frac{a - b - b}{a + b - a}) (x - a) \\ \\ \sf \mapsto y - b = (\frac{a - 2b}{b} )(x - a) \\ \\\sf \mapsto by - {b}^{2} = ax - {a}^{2} - 2bx + 2ba \\ \\\sf \mapsto ax - by - {a}^{2} - 2bx + 2ba + {b}^{2}$

Therefore ,

The equation of the line will be

• ax - by - a² - 2bx + 2ba + b²