Question

Find the distance between the points

Answer 1

Answer with Explanation:

use distance formula to find the distance between two points, as we have given the two points, on a plane (2D)

therefore, We know

$\sf Distance =\sqrt{(y2-y1)^2+</p><p>(x2-x1)^2}$

Here,

P (asinα,acosα) and Q(acosα,-asinα)

$\sf Distance\:of\:PQ=\sqrt{(-asin\alpha-acos\alpha)^2+(acos\alpha-asin\alpha)^2}$

$\implies \sf \sqrt{[(-asin\alpha)^2-2(-asin\alpha)(acos\alpha)+(acos\alpha)^2]+[(acos\alpha)^2-2asin\alpha.acos\alpha+(asin\alpha)^2]}$

$\implies \sf \sqrt{a^2sin^2\alpha+2a^2sin\alpha.cos\alpha+a^2cos^2+a^2cos^2\alpha-2a^2sin\alpha.cos\alpha+a^2sin^2\alpha}$

$\implies \sf \sqrt{a^2sin^2\alpha+a^2cos^2\alpha+a^2cos^2+a^2sin^2\alpha}$

$\implies \sf \sqrt{a^2(sin^2\alpha+cos^2\alpha)+a^2(cos^2α+sin^2\alpha)}$

$\implies \sf \sqrt{a^2+a^2}$

$\implies \sf \sqrt{2a^2}$

$\implies \sf a\sqrt{2}$

Hence the distance between given two points is a√2