Question

Find the distance between the following pair of points:

(asinα, −bcosα) and (−acos α, bsin α)

Answer 1

The distance d between two points (x1, y1) and (x2, y2) is given by the formula.

`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`

The two given points are (asinα, −bcosα) and (−acos α, bsin α)

The distance between these two points is

`d = sqrt((a sin alpha +  a cos alpha)^2 + (- b cos alpha -  bsin alpha)^2)`

`= sqrt(a^2(sin alpha + cos alpha)^2 + b^2(-1)^2(cos alpha + sin alpha))`

`= sqrt(a^2(sin alpha + cos alpha)^2 + b^2(sin alpha + cos alpha))`

`= sqrt((a^2 + b^2)(sin alpha + cos alpha))`

`d = (sin alpha + cos alpha)sqrt(a^2 + b^2)`

Hence the distance is `(sin alpha + cos alpha)sqrt((a^2 + b^2))`