UNIT 5 GEOMETRY5.2 – GRAPH AND WRITE EQUATIONS OF

CIRCLES

GEORGIA PERFORMANCE STANDARDS

• MM3G1A – FIND EQUATIONS OF CIRCLES.• MM3G1B – GRAPH A CIRCLE GIVEN AN EQUATION IN

GENERAL FORM. • MM3G1C – FIND THE EQUATION OF A TANGENT LINE

TO A CIRCLE AT A GIVEN POINT.

VOCABULARY

• A circle is the set of all points (x,y) in a plane that are equidistant from a fixed point, called the center of the circle. The distance r between the center and any point (x,y) on the circle is the radius. The standard form of the equation of a circle with center at (0,0) and radius r

STANDARD FOR OF THE EQUATION OF A PARABOLA WITH VERTEX (0,0) IS AS FOLLOWS:• Graph x2 = 25 – y2

• Steps:• Rewrite the equation

• Identify the center and radius

• Sketch the circle

STANDARD FOR OF THE EQUATION OF A PARABOLA WITH VERTEX (0,0) IS AS FOLLOWS:

• Graph x2 = 25 – y2

WRITE AN EQUATION OF A CIRCLE

• The point (6,2) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.

• Steps:• Where is the origin?• How can we find the distance from the origin to the point?• Put in Standard Form

• x2+y2 = r2

WRITE AN EQUATION OF A CIRCLE• The point (6,2) lies on a circle whose center is the origin. Write

the standard form of the equation of the circle.

GUIDED PRACTICE: PAGE 180: 1-4

• REMEMBER TO GRAPH!! • REFER TO YOUR NOTES FOR HELP!!

FIND AN EQUATION OF A LINE TANGENT TO A CIRCLE• Find an equation of the line tangent to the circle x2 + y2 = 10

at (-1,3)

• Some things that can help….• A line tangent to a circle is perpendicular to the radius at the point

of tangency• Slope formula:

• Point slope formula:

• How can you tell if a line is perpendicular? Negative Reciprocal

FIND AN EQUATION OF A LINE TANGENT TO A CIRCLE

• Find an equation of the line tangent to the circle x2 + y2 = 10 at (-1,3)

WRITE A CIRCULAR MODEL• A furniture store advertises free delivery up to a 50 mile radius from the

store. If a customer lives 28 miles east and 41 miles north of the store, does the customer qualify for free delivery?

GUIDED PRACTICE: PAGE 181: 5 & 6