# Deriving the Equation of a Circle

## INTRODUCTION

Equations represents figures in the Cartesian plane. A “line” is represented by a linear function

**, while a “parabola” is represented by a quadratic function***y = mx + b***. This activity aims to find the equation that will represent a “Circle” in the Cartesian plane, thus the derive the equation of a circle.***y = (x-h)*^{2}+ kThe figure above is a right triangle. Given that its hypotenuse

**is constantly equal to 5, try to rotate point***r***.***P*What figure did you formed?

What is the radius of the figure you formed?

As you can observe, the values of

**and***x***changes as you move point***y***forming a circle.***P*Give an equation that will represent the relationship between ** x** and

**such that it will form a circle**

*y**(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)