Question

find the distance......??​

Answer 1

$\small{\underline{\sf{\blue{Given\:Points:\rightarrow}}}}$

• P (asinα,acosα) and Q(acosα,-asinα)

$\small{\underline{\sf{\orange{To\:Find:\rightarrow}}}}$

• Distance between PQ

$\small{\underline{\sf{\pink{Solution:\rightarrow}}}}$

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

therefore, We know

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

Here,

P (asinα,acosα) and Q(acosα,-asinα)

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

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

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

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

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

➱Hence the distance between given two points is a√2

Answer 2

Answer:

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

therefore, We know

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

Here,

P (asinα,acosα) and Q(acosα,-asinα)

⇝DistanceofPQ=(−asinα−acosα)2+(acosα−asinα)2

⟹a2(sin2α+cos2α)+a2(cos2α+sin2α)

⟹a2+a2

⟹2a2

⟹a2

Hence the distance between given two points is a root 2