Question

find the distance between the point (acosteta,0) and (0,asinteta)​

Answer 1

$\maltese$Given to find the  distance between the points $(acos\theta, 0) \:and (0, asin\theta)$

$\maltese$SOLUTION :-

For finding the distance between the two points(x_1, y_1) and (x_2, y_2) we have formula that is

$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Putting down the values in formula

$x_1 = acos\theta\\x_2 = 0$

$y_1 = 0 \\y_2 = asin\theta$

So, distance between them is

$= \sqrt{(acos\theta-0)^2+(0-asin\theta)^2}$

$=\sqrt{(acos\theta)^2+(-asin\theta)^2}$

$=\sqrt{a^2cos^2\theta+a^2sin^2\theta}$

Take common a²

$= \sqrt{a^2(cos^2\theta+sin^2\theta)}$

As we know from trigonometric identities sin²A+cos²A= 1

$=\sqrt{a^2(1)}$

$= \sqrt{a^2}$

$= a$

${\boxed{The\:  distance\: between\: the\: points (acos\theta, 0) \:and (0, asin\theta) \: is \: a\: units}}$

Know more :-

Centroid formula:-

$\bigg(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\bigg)$

Section formula Internal division:-

$\bigg(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\bigg)$

Section formula External division:-

$\bigg(\dfrac{mx_2-nx_1}{m-n}, \dfrac{my_2-ny_1}{m-n}\bigg)$

Mid point formula:-

$\bigg(\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2}\bigg)$