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)

$$\text{ Here },(x_1,y_1)\equiv (a,b)$$

$$(x_2,y_2)\equiv (a+b,a-b)$$

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

$$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$$

$$\Rightarrow y-b=\frac{a-b-b}{a+b-a}(x-a)$$

$$\Rightarrow by-b^2=(a-2b)x-a^2+2ab$$

$$\Rightarrow (a-2b)x-by+b^2+2ab-a^2=0$$