Chapter 9 Section 8: Equations of Circles

Remember the distance formula? Distance = Use the distance formula to find the radius of the circle. **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: Standard Equation of a Circle: _______________ where (h,k) is the _________ and r is the ________. The equation of the Circle C with center (-1,4) is: _______________ Radius= 5 2 2 2 (x – h) + (y – k) = r center radius 2 2 (x + 1) + (y – 4) = 25

with center C(-3, 6) and a y = (x + 2) + (y – 3) = 10 Examples: Write an equation for a circle 2. Graph the circle whose equation is with center C(-3, 6) and a y = (x + 2) + (y – 3) = 10 radius of 6 units. Graph it. 2 2 2 2 (x + 3) + (y – 6) = 36 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. 5. center: _______ center: _________ center: ________ radius: _______ radius: _________ radius: _________ (3/4, -3) (-4, 0) (0, 0) 9/2 or 4.5 11 2.83 Write an equation of Circle P based on the given information. 6. Center: P(0,0); 7. Center: P(-1, 4); radius radius: radius: 8. Center: P(0,- ) 5 2 2 2 2 2 x + y = 25 (x + 1) + (y – 4) = 15 2 x + (y + 1.5) = 16/9

That's all! Assignment: Equation of circles ws