Find the equation of the straight lines passing through the following pair of point: `(a , b)a n d\ (a+csinalpha,\ b+c\ cosalpha)`

Explanation

`(x_1, y_1) = (a, b), (x_2, y_2) = (a + c sin α, b + c cos α)`

So, the equation of the line passing through the two points `(0, 0)` and `(2, −2)` is

By using the formula,
`y-y_1=frac{y_2-y_1}{x_2-x_1}(x-x_1)`

Substitute the values, we get `y-b=frac{b+c cos alpha-b}{a+c sin alpha-a}(x-a)`

`y-b= cot alpha(x-a)`