Advanced Algebra H Notes Section 9.3 – Graph and Write Equations of Circles Objective: Be able to graph and write equations of circles. A _________ is the set of points (x, y) in a plane that are equidistant from a fixed point, called the ___________ of the circle. The distance r between the center and any point on the circle is called the ___________. Example 1: Graph and identify the radius and center of the circle. x 2 – 4 = - y 2 circle center radius

Example 2: Write an equation of a circle. The point (-4, 7) lies on a circle whose center is the origin. ** Recall from Geometry that a line tangent to a circle is perpendicular to the radius at the point of tangency. Example 3: Write an equation of a line tangent to a circle. What is the equation of the line tangent to the circle x 2 + y 2 = 61 at (5, -6). A line tangent to a circle is perpendicular to the radius at the point of tangency. The radius to the point (5, -6) has a slope of: The slope of the tangent line is perpendicular to that,so its slope is:

Standard Equation of a Circle with Center at (h, k) (x – h) 2 + (y – k) 2 = r 2 Example 4: Write an equation for the circle graphed below.

Example 5: Graph the circle and state its center and radius. x 2 + y 2 - 2x + 4y + 1 = 0 C(1, -2) r = 2