Conics Lesson 2: Circles Mrs. Parziale. Circles Circle – the set of all points at a given distance from a central point CENTER = (h, k)RADIUS = r Equation.

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Conics Lesson 2: Circles Mrs. Parziale

Circles Circle – the set of all points at a given distance from a central point CENTER = (h, k)RADIUS = r Equation for circles: r 2 = (x – h) 2 + (y – k) 2 h, k, r are all NUMBERS x, y are VARIABLES

Example 1: Given the equation x 2 + y 2 = 49 What is the center? What is the radius? Sketch it.

Example 1: Given the equation (x – 4) 2 + (y + 3) 2 = 9 What is the center? What is the radius? Sketch it.

Example 1: Given the equation (x + 2) 2 + (y – 2) 2 < 9 What is the center? What is the radius? Sketch it.

Example 4: Given a circle with center at (0, -1) and a radius of 1. Write a simplified equation for the circle. r 2 = (x – h) 2 + (y – k) 2 h = ____ k = ____ r 2 = ____

Example 5: Write the equation for a circle with a center at (1, 2) and containing the point (3, 4). r 2 = (x – h) 2 + (y – k) 2 (h, k) = (x, y) =

Example 6: Given the equation of a circle, What is the center? What is the radius?

Closure For the equation Find the radius. Find the center. Sketch it.