We will only look at Circles and Parabolas this year

(x, y) r y x We find the equation of a circle from where the center is and the distance from the center to a point on the circle (the radius).

The equation is found using the Pythagorean Theorem Center: (h, k) Radius: r

Find the radius and graph. 6x 2 + 6y 2 = 60 Center at the origin x 2 + y 2 = 36

(x-2) 2 + y 2 = 16 Center: ________ r: ______ 2(x+3) 2 + 2(y+2) 2 = 50 Center: ________ r: ______ translated Center that is translated Find the center, radius and graph.

Getting an equation into standard form To write the standard equation of a translated circle, you will need to complete the square. To write the standard equation of a translated circle, you will need to complete the square.

Getting an equation into standard form Example: Center: (4, 0) r: 3 To write the standard equation of a translated circle, you will need to complete the square. To write the standard equation of a translated circle, you will need to complete the square.

Example!!! Write the standard equation for the circle. State the center and radius.

Now we will work backwards and find the equation of a circle

Write the equation of a circle with the given radius and whose center is the origin.

Example: Write the standard equation for the translated circle with center at (-2, 3)and a radius of

Another one Write the equation of the circle with the center (3,-1) and the radius. *Always look for Center: _______ and Radius: _____

Writing equations given a point You must find the radius 1 st using the distance formula

*Always look for Center: _______ and Radius: _____ Write the equation of the circle with the point (4,5) on the circle and the origin as it’s center.

Find equation of circle passing through (5, 1) with the center at (2,-3)

Find equation of circle with diameter ending at points (5,3) and (-3, 13).

Last thing! Verifying if a point lies on a circle Plug the point into the equation of the circle and see if the resulting equation is true

Example