Circle- the set of all points (x,y) in a plane that are ...



Circle Notes Name___________________________

Circle- the set of all points (x,y) in a plane that are equidistance from a fixed point called the center of the circle.

Radius- distance from center to any point on the circle.

Standard Equation of a Circle with Center at the origin

x2 + y2 = r2 ; where r is the radius

Graphing Circles:

Graph y2 = -x2 + 36

Step 1: Rewrite x2 + y2 = 36

Step 2: Find the radius= 6

Step 3: Plot 6 units from origin in all directions on the x and y axis. Draw circle.

Writing Equation of a Circle

The point (2, -5) lies on a circle whose center is the origin. Write the equation of the circle.

Step 1: Find the radius by using the distance formula and the center (0,0) and

point (2, -5)

Radius = [pic]

Step 2: Write the equation of the circle x2 + y2 = 29

Writing the Equation of a line tangent to a circle.

Write the equation of the line tangent to the circle x2 + y2 = 13 at (-3,2).

Solution: A line tangent to a circle is perpendicular to the radius at the point of tangency. Because the radius to the point (-3,2) has a slope of -2/3, the slope of the tangent line at

(-3,2) is the negative reciprocal of -2/3 or 3/2. An equation of the tangent line is as follows:

[pic]

Circles and Inequalities- The regions inside and outside the circle x2 + y2 = r2 can be described by inequalities, with x2 + y2 < r2 represents the region inside the circle and

x2 + y2 > r2 represents the region outside the circle.

Problem: A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles east and 9 miles south of the tower. Are you in the tower’s range?

Suppose you fix the tire and then drive south. . For how many more miles will you be in the range of the tire?

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