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