How To Graph A Circle Using The General Equation: Center, Radius, And Coordinates Explained

Equation of a circle

(x-h)²+(y-k)²=r²

The general equation for a circle with center at (h, k) and radius r is:

(x – h)^2 + (y – k)^2 = r^2

Where:

– (x, y) represents any point on the circle’s circumference.
– (h, k) represents the center of the circle.
– r represents the radius of the circle, which is the distance from the center to any point on the circumference.

If the circle is centered at the origin (0, 0), the equation simplifies to:

x^2 + y^2 = r^2

This equation can be used to graph a circle on a coordinate plane. To do so, plot the center point (h, k) and then use the radius r to plot points on the circle’s circumference, by solving the equation for x and y for different values of theta and substituting these values into the equation:

x = h + r cos(theta)
y = k + r sin(theta)

Where theta is the angle measured from the positive x-axis to the point (x, y) in a counterclockwise direction. By plotting enough points, a smooth curve can be drawn to represent the circle.

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