Question

find the equation of the line passing through the points (a cosalpha ,a sinalpha ) and ( a cosbeta ,a sinbeta) ​

Answer 1

Answer:

$\frac{y - a.sin \alpha }{x - a.cos \alpha } = \frac{a.sin \beta - a.sin \ \alpha }{a.cos \beta - a.cos \alpha }$

$\frac{y - a.sin \alpha }{x - a.cos \alpha } = \frac{sin \beta - sin \ \alpha }{cos \beta - cos \alpha }$

$y.cos \beta - y.cos \alpha \\ - a.sin \alpha .cos \beta + a.sin \alpha .cos \alpha \\ = x.sin \beta - x.sin \alpha \\ - a.cos \alpha .sin \beta + a.cos \alpha .sin \alpha$

$x(sin \beta - sin \alpha ) + y(cos \alpha - cos \beta ) \\ + a.(sin \alpha .cos \beta - sin \beta .cos \alpha ) = 0$