10-8 Equations of Circles 1.Write the equation of a circle. 2.Graph a circle on the coordinate plane.

Equation of a Circles Since all points on a circle are equidistant from the center, you can find an equation of a circle by using the Distance Formula. r 2 = (x – h) 2 + (y – k) 2 r = distance (h, k) = the point representing the center of the circle. (x, y) = the point on the circle. The standard form of the equation of a circle is also called center-radius form.

Example 1: Write the equation of the given circle. Center at the origin; radius. What’s the formula for the equation of a circle? r 2 = (x – h) 2 + (y – k) 2 Substitute: (x – 0) 2 + (y – 0) 2 10 = x 2 + y 2

Example 2: Write the equation of the given circle. Center at (4, -1); diameter 8 What’s the formula for the equation of a circle? r 2 = (x – h) 2 + (y – k) 2 Substitute: (x – 4) 2 + (y + 1) = 16 = (x – 4) 2 + (y + 1) 2

Example 3: Write the equation of the given circle. Center at (5, 4); passes through (-3, 4) Substitute: (x – 5) 2 + (y - 4) = 64 = (x – 5) 2 + (y - 4) 2 We need the radius. Remember radius is the distance, so use the distance formula to find the radius. What’s the formula for the equation of a circle? r 2 = (x – h) 2 + (y – k) 2

Example 4: For the circle with the equation (x + 4) 2 + (y – 5) 2 = 25, state the coordinates of the center and the measure of the radius. Then graph the equation. (h, k) is the center of the circle. r 2 = (x – h) 2 + (y – k) 2 (-4, 5) The radius is always on the side of the equation by itself. You must take the square root of it. r = Graph the center of the circle. 2. Plot the radius (both horizontal and vertical). 3. Draw the circle using your compass...