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# Find the Distance Between the Following Pair of Points: (Asinα, −Bcosα) and (−Acos α, Bsin α) - CBSE Class 10 - Mathematics

#### 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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Solution Find the Distance Between the Following Pair of Points: (Asinα, −Bcosα) and (−Acos α, Bsin α) Concept: Distance Formula.
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