## Algebra

To find the centre of the circle, we need to complete the square for both the x and y terms. This will give us the coordinates of the centre of the circle. Let’s walk through the steps together.

### solving equations

In mathematics, an equation is a statement of equality containing one or more variables. Solving equations is the process of determining which values of the variables make the equation true. There are many ways to solve equations.

The most basic way to solve an equation is to use algebraic manipulation to isolate the variable on one side of the equation and then determine what value(s) of the variable make the equation true. This can be done by using the addition, subtraction, multiplication, or division properties of Equality.

Another way to solve equations is to graph both sides of the equations on a coordinate plane, and then determine where the two lines intersect. The coordinates of the point of intersection will be the solution to the equation.

There are also a variety of methods that can be used to solve systems of linear equations with two or more variables. These methods include substitution, elimination, and matrices.

### graphing linear equations

A linear equation is any equation that can be written in the form ax+by=c. To graph a linear equation, we can use the slope-intercept form, which is written as y=mx+b. In this form, m is the slope and b is the y-intercept. To find the y-intercept, we let x=0 and solve for y. To find the slope, we take two points on the line and use the formula m=(y2-y1)/(x2-x1).

## Circles

To find the center of a circle, we need to use the equation of the circle. The equation of a circle is (x-h)^2 + (y-k)^2= r^2 . In this equation, (h,k) is the center of the circle, and r is the radius.

### graphing circles

To graph a circle, start by plotting the center of the circle. Then, use a ruler or compass to draw a line segment from the center out to any point on the circle. Doing this will give you the radius of the circle. Finally, use your ruler or compass to complete the rest of the circle by drawing an arc that is exactly the same distance from the center as the original line segment.

### finding the center of a circle

To find the center of a circle whose equation is in the form x^2 + y^2 = r^2, first square both sides of the equation. This will give you an equation in the form (x^2/r^2) + (y^2/r^2) = 1. Next, take the square root of both sides of the equation. This will give you an equation in the form sqrt((x^2/r^2) + (y^2/r^2)) = 1. Finally, solve for x and y. The solutions will be the coordinates of the center of the circle.