Understanding the Equation of a Circle: Explained with Examples and Formats

equation of a circle

The equation of a circle is given by:

(x – h)^2 + (y – k)^2 = r^2

Where:
– (h, k) represents the coordinates of the center of the circle

The equation of a circle is given by:

(x – h)^2 + (y – k)^2 = r^2

Where:
– (h, k) represents the coordinates of the center of the circle.
– r represents the radius of the circle.

Let’s break down the elements of this equation:

1. (x – h) represents the horizontal distance from any point (x, y) on the circle to the center, h. This term is squared to eliminate the negative sign.
2. (y – k) represents the vertical distance from any point (x, y) on the circle to the center, k. This term is squared to eliminate the negative sign.
3. r^2 represents the squared radius of the circle.

To use this equation, you need to know the coordinates of the center (h, k) and the radius, r.

For example, let’s say we want to find the equation of a circle with center (2, -3) and radius 5. Plugging in the values into the equation, it becomes:

(x – 2)^2 + (y – (-3))^2 = 5^2

Simplifying further:

(x – 2)^2 + (y + 3)^2 = 25

This is the equation of the circle with center (2, -3) and radius 5.

Note: In some cases, you might encounter a slightly different format of the equation, where it is written as:

(x – a)^2 + (y – b)^2 = c

In this case, the center of the circle would be (a, b), and the radius would be the square root of c.

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