Sec 1.8 Circles Objectives: To understand the distance and midpoint formulas. To understand the equations of circles and their graphs.

Distance Formula The distance between the points A(x 1, y 1 ) and B(x 2, y 2 ) in the plane is:

Ex 1. Find the distance between (-2,8) and (4,-4)

Midpoint Formula The midpoint of the line segment from A(x 1, y 1 ) to B(x 2, y 2 ) is:

Ex 2. Find the midpoint between (-2,8) and (4,-4)

Class Work 1.Which of the points P(1, –2) or Q(8, 9) is closer to the point A(5, 3)? 2.Show that the quadrilateral with vertices P(1, 2), Q(4, 4), R(5, 9), and S(2, 7) is a parallelogram by proving that its two diagonals bisect each other.

Definition of a Circle A circle is the set of all points P(x, y) whose distance from the center C(h, k) is r.

Equation of a Circle The equation of a circle with center (h,k) and radius r is given by:

Ex 3. Find the equation of a circle with center (2, -5) and radius 3.

Ex 4. Show that the equation represents a circle, and find the center and radius of the circle. x 2 – 6x +y 2 – 2y = 43

Class Work 3. Find the equation of a circle that has endpoints of a diameter that are P(-1, 1) and Q(5, 9). 4. Show that x 2 + y 2 + 2x – 6y + 7 = 0 is a circle and find the center and radius.

Class Work 5. Show that x 2 + y 2 + 6y + 2 = 0 is a circle and find the center and radius. 6. Show that 3x 2 + 3y 2 + 6x – 12y = 0 is a circle and find the center and radius.

HW p odd, 27,29, odd