Question

find the distance between
A(a sinalpha,-b cosalpha),B(-a cosalpha,b sinalpha)

Answer 1

 d=sqrt[ (p sin alpha- ( -pcos alpha))^2+ ( -q cos alpha- ( -q sin alpha))^2]

= sqrt[ p^2 sin ^2 alpha+p^2 cos^2alpha +2p^2sin alpha*cos alpha+q^2 sin ^2 alpha+q^2 cos^2alpha +2q^2sin alpha*cos alpha]

=sqrt [ sin ^2alpha(p^2+q^2)+ cos^2alpha (p^2+q^2)+2sin alpha*cos alpha (p^2+q^2)

=sqrt [ (p^2+q^2) {sin ^2 alpha+ cos^2alpha +2sin alpha*cos alpha}]

=sqrt [ (p^2+q^2){sin alpha+cos alpha}^2

{sin alpha+cos alpha}sqrt [ (p^2+q^2)

Answer 2

See the attachment …......