Circles in the Coordinate Plane Equation of a

Circles in the Coordinate Plane

Equation of a Circle Standard Equation of a Circle: An equation of a circle with center (h, k) and radius r is (x – h)2 + (y – k)2 = r 2.

Writing the Equation of a Circle • What is the standard equation of a circle with center (5, -2) and radius 7?

What is the standard equation of each circle? • Center (3, 5); radius 6 • Center (-2, -1); radius 2

Using the Center and a Point on a Circle • What is the standard equation of the circle with center (1, -3) that passes through the point (2, 2)?

What is the standard equation of the circle with center (5, 3) that passes through the point (-1, 1)?

Graphing a Circle Given Its Equation • Graph the circle whose equation is (x + 4)2 + (y – 1)2 = 25.

Completing the Square Recall that we can solve quadratic equations of the form ax 2 + bx + c = 0 by “completing the square”… 1. Subtract c from both sides. ax 2 + bx = - c 2. Square half the coefficient of x and add it to both sides. ax 2 + bx + =-c+ 3. Then “un-FOIL” We can use this process to find the standard equation of circles when given the “FOILed” equation.

Completing the Square to Find the Equation of a Circle Find the center and radius of the circle whose equation is x 2 + y 2 – 8 x + 6 y + 5 = 0.

Find the center and radius of a circle whose equation is x 2 + y 2 + 8 x – 6 y – 15 = 0.