10 3 Circles Algebra 2 Definition n Circle

10. 3 Circles Algebra 2

Definition: n Circle: The set of all points (x, y) that are equidistant from a fixed point, called the center of the circle. The distance r between the center of the circle and any point (x, y) on the circle is the radius

Diagram of a Circle

Standard Equation Of A Circle (Center at origin) n The standard form of the equation of a circle with center at (0, 0) and a radius r is as follows…

Example: n Draw the graph of n Draw the circle given by

Additional Examples

Examples: n (-2, 5) is on a circle centered at the origin. Write the equation of the circle. n (5, 1) is on a circle centered at the origin. Write the equation of the circle.

More Examples:

Geometry Theorem n A line tangent to a circle is perpendicular to the circle’s radius at the point of tangency

Example: n Write an equation of the line that is tangent to the circle at (1, 4)

Example: n Write an equation of the line that is tangent to the circle at (-2, 4)

Additional Examples:

Examples: n A street light can be seen on the ground within 30 yd of its center. You are driving and are 10 yd south of the light. ¡ ¡ Write an inequality to describe the region on the ground that is lit by the light. Is the street light visible?

Example: n In the last example, you are driving due north. For how many more yards will you be able to see the beam?

Example: n You are sky diving and are trying to land on a target with a radius of 15 m. You land 10 m north of the center of the target. ¡ ¡ ¡ Write an inequality to describe the region inside the target area. Do you land within the target area? If another skydiver lands 4 m east and 14 m north of the center of the target, who is closer to the center?