Question

G（b,a²）,H（a,b²）求两点所过直线的倾斜角

Answer 1

G（b,a²）,H（a,b²）求过此两点的直线的倾斜角α

tanα=(b²-a²)/(a-b)=(b+a)(b-a)/(a-b)=-(a+b)

故α=arctan[-(a+b)]=π-arctan(a+b)

tanα=tan[π-arc tan(b+a)]=-tanarctan(a+b)=-(a+b)

而tan[π+arc tan(b+a)]=tanarctan(a+b)=a+b

∴α=π-arctan(a+b).