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Deriving the Equation of a Circle


Equations represents figures in the Cartesian plane. A “line” is represented by a linear function y = mx + b, while a “parabola” is represented by a quadratic function y = (x-h)2 + k. This activity aims to find the equation that will represent a “Circle” in the Cartesian plane, thus the derive the equation of a circle.
The figure above is a right triangle. Given that its hypotenuse r is constantly equal to 5, try to rotate point P.

What figure did you formed?

What is the radius of the figure you formed?

As you can observe, the values of x and y changes as you move point P forming a circle.

Give an equation that will represent the relationship between x and y such that it will form a circle (Note: remember that we started with a right triangle)

The equation you formed already represent a circle with radius of 5.

Now, give the general equation that will represent a circle with any radius r.

Your answer is the general equation for a circle given that its center is at the origin (0,0)