5.2 Graph and Write Equations of Circles Pg 180

A circle is an infinite set of points in a plane that are equal distance away from a given fixed point called a center. A radius is a segment that connects the center and one of the points on the circle. Every radius is equal in length. (radii) A diameter is a line segment that connects two points on the circle and goes through the center.

The formula for a circle with its center at (0,0) and a radius of “r” is: Example: What is the equation for a circle whose center is at (0,0) and has a radius of 6. Answer ?

Example #2: Identify the center and the radius of the following: Answer ? Center: (0,0) Radius 10

Write an equation for the following in standard form.

Graph the Equation of a Circle Graph x2 = 25 – y2

Write an Equation of a Circle The point (6, 2) lies on a circle whose center is the origin. Write the standard form of the equation of the circle. We need to find the radius. Use the distance formula.

If a circle has a translated center then the new equation will be: Where the new center will be (h, k) and “r” will be the radius.

Example #1. Write the standard equation for a circle whose center is at (-3,5) and has a radius of 7. Answer: Since h=-3 and k=5 and r=7 we can substitute these into the equation Therefore: Or:

Example #2 Given the following equation, identify the center and the radius. Did you say (7,-2) Radius ? I bet you said (drum roll please) 9 You guys are AWESOME !!!

Example #3 Given the following graph answer the following questions. 1. Identify the center. 2. Name the radius. 3. Write an equation in standard form for the circle.

Answers Center: (-2,-1) Radius: 8 Equation:

Finding the equation of a Tangent Line to a Circle Any line tangent to a circle will be perpendicular to a line that goes through the tangent point and the center of the circle Perpendicular lines have negative reciprocal slopes (Opposite Reciprocal) So if we have the center of a circle, and the point of tangency, we can find the slope by the slope formula Take the negative reciprocal and use the point slope formula for a line that goes through the tangent point

Find the equation of a Tangent Line to a circle Find the equation of a tangent line to the circle x2 + y2 = 10 at (-1, 3)

Assignment Pg 182 1 – 23, 24 odd Pg 183 1 – 17, 18 odd