Sect. 12-1 Circles in the Coordinate Plane Geometry Honors.

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Presentation transcript:

Sect Circles in the Coordinate Plane Geometry Honors

What and Why? What? – Write the equation of a circle. – Use the equation of a circle to solve real world problems. Why? – To investigate situations in which equations of circles can be used, such as expressing the range of cellular telephone towers.

Distance Formula

Theorem 12-1 Equation of a Circle

Example

When you make a call from your cell phone, a tower receives the call. In the graph, the center of each circle is the location of a cell tower. The equation of a circle can describe the receiving and transmitting range of a tower. Find the equation that describes the position and the range of Tower A.

Example If you know the center of a circle and a point on the circle, you can write the equation of the circle. Write an equation of the circle with center (1, -3) that passes through the point (4, 2).

Example

Write an inequality for the given graph.

Example A diameter of a circle has endpoints (-3, 7) and (5, 5). Write an equation of the circle.