Equations represents figures in the Cartesian plane. A “line” is represented by a linear function [b][i]y = mx + b[/i][/b], while a “parabola” is represented by a quadratic function [b][i]y = (x-h)[sup]2[/sup] + k[/i][/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.
The figure above is a right triangle. Given that its hypotenuse[b][i] r[/i][/b] is constantly equal to 5, try to rotate point [b][i]P[/i][/b].
What figure did you formed?
What is the radius of the figure you formed?
As you can observe, the values of [b][i]x[/i][/b] and [b][i]y[/i][/b] changes as you move point [b][i]P [/i][/b]forming a circle.
Give an equation that will represent the relationship between [b][i]x[/i][/b] and [b][i]y[/i][/b] such that it will form a circle [i](Note: remember that we started with a right triangle)[/i]
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 [b][i]r[/i][/b].
Your answer is the general equation for a circle given that its center is at the origin (0,0)