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Question
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Solution
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))`
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