# ﻿Find Y at X on the circumference of a circle, centered at (0,0)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

We have the circle centered at O(0,0)

r is the radius.

==> x^2 + y^2 = r^2

(x,y) is a point on the corcumference)

There are unlimited points on the cicumference of the circle.

However, the relation between x and y should be constant and defines with the equation x^2 +y^2 = r^2

Points on the circumference could be:

(r,0) (0, r) ( -r,0) (0, -r)

Also, y= sqrt(r^2 - x^2)

Top Answer

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let P(x,y) be a point on the circumference of a circle  whose radius is r and centre O(0,0).

Draw a perpendicular from P to X axis to meet at X

Then OP^2 = OX^2 +XP^2

r^2 = x^2 +y^2. As OX is x coordinate anf XP is y coordinate, and OP= r, the radius of the circle.

Therefore y^2 = r^2 -x^2

y = + sqrt(r^2-x^2) or

y = -sqrt(r^2-x^2)

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