28. Writing Equations of Circles

CONIC SECTIONS

(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. Circles Center at the origin Find the radius and graph. x2 + y2 = 36 6x2 + 6y2 = 60

Center that is translated Circles Center that is translated Find the center, radius and graph. (x-2)2 + y2 = 16 Center: ________ r: ______ 2(x+3)2 + 2(y+2)2 = 50 Center: ________ r: ______

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

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

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 1st using the distance formula

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

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

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