Find the equation of the straight lines passing through the following pair of point: `(a\ cosalpha,\ asinalpha)a n d\ (a\ cosbeta,\ asinbeta)`

Explanation

The equation becomes,

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

`y-a sin alpha=frac{a sin beta-a sin alpha}{a cos beta-a cos alpha}(x-a cos alpha)`

`y-a sin alpha=frac{sin beta-sin alpha}{cos beta- cos alpha}(x-acos alpha)`

`y(cos beta-cos alpha)-x(sin beta-sin alpha)-a sin alpha cos beta-a sin alpha cos alpha+a cos alpha sin beta-a cos alpha sin alpha=0`

`2y sin(frac{alpha+beta}{2})sin(frac{alpha-beta}{2})+2xsin(frac{beta-alpha}{2})cos(frac{alpha+beta}{2})=2a sin(frac{alpha-beta}{2}) cos(frac{alpha-beta}{2})`

`x cos(frac{alpha+beta}{2})+y sin(frac{alpha+beta}{2})=a cos (frac{alpha-beta}{2})`