Question

find the distance between (-a cos Φ, b sinΦ) and (a sin Φ, -b cos Φ)

Answer 1

AB =√(x2-x1)²+(y2-y1)²

x1 = -a cosΦ, y1 = b sinΦ
x2 = a sinΦ, y2 = -b cosΦ

Put the value in the equation
AB = √(a sinΦ + a cosΦ)2 + (-b cosΦ - b sinΦ)2
AB =(sinΦ + cosΦ)√(a2+b2)