Chapter 9 Section 8 Equations of Circles Remember

Chapter 9 Section 8: Equations of Circles

Remember the distance formula? Distance = Use the distance formula to find the radius of the circle. Radius= 5 **Remember, you can also make a right triangle on the coordinate plane and use Pythagorean Theorem! Once we find the radius, we can use it and the center to find the equation of a circle: 2 2 2 (x – h) + (y – k) = r Standard Equation of a Circle: ________ center radius where (h, k) is the _____ and r is the ____. (x + 1) 2+ (y – 4)2= 25 The equation of the Circle C with center (-1, 4) is: ________

Examples: 1. Write an equation for a circle with center C(-3, 6) and a 2. Graph the circle whose equation is 2 y = (x + 2) + (y – 3) = 10 radius of 6 units. Graph it. (x + 3)2 + (y – 6)2 = 36 2 Center: (-2, 3) Radius: 3. 16

Determine the coordinates of the center and the measure of the radius for each circle whose equation is given. 3. 4. (3/4, -3) center: _______ 9/2 or 4. 5 radius: _______ (-4, 0) center: _____ 11 radius: _____ 5. (0, 0) center: ____ 2. 83 radius: _____ Write an equation of Circle P based on the given information. 6. Center: P(0, 0); radius 5 2 2 x + y = 25 7. Center: P(-1, 4); radius: 2 (x + 1) + (y – 4)2 = 15 8. Center: P(0, - ) radius: 2 x + (y + 1. 5)2 = 16/9

Assignment: Equation of circles ws