Conic Sections Circles Objective: Find the standard form of a circle

Review Find an equation to represent the set of points equidistant from (2, 4) with a radius of 6. Use distance formula.

General Equation of a Circle Find the equation that represents the set of points equidistant from (h, k) with radius r. Given the equation of a circle, find its center and radius to graph the circle. (x – 5) 2 + (y + 1) 2 = 16

Conics A circle is one type of conic section. Conic sections are formed by the intersection of a double tipped cone with a plane. Cut horizontally, the intersection is a __________. Cut vertically, the intersection is a _____________. Cut diagonally to intersect one cone completely is a ________. Cut diagonally to intersect one cone only partially is a ________.

Circles Find the center and radius of the circle. 1. (x – 2) 2 + (y – 6) 2 = x 2 + (y + 8) 2 = x 2 + y 2 = 100 Give the equation of the circle with radius (1, 5) and r = 3.

Completing the Square Find the center and radius of the circle x 2 + y 2 – 8x + 10y + 24 = 0. Gather the x’s and y’s and complete the square. x 2 – 8x + y y = -24 Practice: Find the radius and center of the circle x 2 + y x – 8y + 3 = 0

Given a Center and a Point… Find the equation of the circle with its center at (5, 10) that goes through the point (7, 11). (x – h) 2 + (y – k) 2 = r 2 We know the center, we need the radius. How would you find the radius?

Practice BINGO Make a 4 x 4 grid and fill in the squares with the following answers in any order: (4,5) r=√2(-3/2, -5/2) r=5/2(-4, -2) r=6(2, 6) r=7 (3, 0) r = 4(1, 0) r = 4(-4, 0) r = 10(2, -1) r=4 (-11, 1) r = 5(4, -1) r=√2(5, 0) r=4(0, 0) r=10 (0, 4) r=√10(-2, -2) r = 2(-3, 2) r=2(3, 1) r = 6

Assignment - Worksheet