Question

Find the equation of the straight lines passing through the following pair of point :

(a, b) and (a + b, a − b)

Answer 1

(a, b) and (a + b, a − b)

\[\text { Here }, \left( x_1 , y_1 \right) \equiv \left( a, b \right) \]

\[\left( x_2 , y_2 \right) \equiv \left( a + b, a - b \right)\]

So, the equation of the line passing through the two points is

\[y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}\left( x - x_1 \right)\]

\[ \Rightarrow y - b = \frac{a - b - b}{a + b - a}\left( x - a \right)\]

\[ \Rightarrow by - b^2 = \left( a - 2b \right)x - a^2 + 2ab\]

\[ \Rightarrow \left( a - 2b \right)x - by + b^2 + 2ab - a^2 = 0\]