Warm up O Find the coordinates of the midpoint of the segment that has endpoints at (- 5, 4) and (7, - 2). O Find the distance between points at (10,

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Warm up O Find the coordinates of the midpoint of the segment that has endpoints at (- 5, 4) and (7, - 2). O Find the distance between points at (10, 7) and (- 4, 8)

Lesson 10-2 Circles Objective: To use and determine the standard and general forms of the equation of a circle To graph circles

Conic Sections Formed when a plane intersects a double right cone.

Degenerate Conics O formed when the plane passes thru the vertex of the double right cone. degenerate ellipse degenerate hyperbola degenerate parabola

Circle O a set of points in a plane which are equidistant from a given point. (the center) O Radius – the distance from the center to any point on the circle.

Circle O The Standard Form of a circle with a center at (0,0) and a radius, r, is…….. O From Pythagorean Theorem center (0,0) radius = 2 Copyright ©1999-2004 Oswego City School District Regents Exam Prep Center

Circles Now if the center moves off of the origin to point (h, k) we can use the distance formula to find the radius. (x, y) (h, k)

Circles O The Standard Form of a circle with a center at (h,k) and a radius, r, is…….. center (3,3) radius = 2 Copyright ©1999-2004 Oswego City School District Regents Exam Prep Center

Example 1 O Write the standard form of the equation of the circle that is tangent to the x-axis and has its center at (-5, 4). Then graph the equation.

Example 2 O The equation of a circle is: Write the standard form of the equation. divide by 4 complete the square

Example 2 cont’d

Example 3 O Write the standard form of the equation of the circle that passes through the points at (1,1), (1, 2), and (2, 3). Then identify the center and radius of the circle. O Use the general equation O Use each point as x and y to create 3 new equations and solve the system for D, E and F. O Once found substitute D, E and F back into the original equation and complete the square (twice) to create the equation of the circle.

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