Math 3 College Prep

Unit 10: Geometry Part II

Standard Form Equation of a Circle: (𝒙  center: (𝒉, 𝒌)  radius: r

Day 5: Equations of Circles

𝒉)𝟐

(𝒚

𝒌)𝟐

𝒓𝟐

Examples Write the equation of the circle in standard form. 1. 2.

3.

equation:

equation:

equation:

___________________________

___________________________

___________________________

Graph the circle. ) ( 4. (

5.

)

(

)

(

)

6.

(

)

Write the equation of the circle with the given information. 7. center: (-8, -2) ; radius: 7

8. center: (5, 0) ; radius: 2

9. center: (0 , 0); diameter: 18

What if the radius and center are not directly stated??? 



distance formula can be used to find the radius  given the center and the end point of the radius/a point on the line  given both end points of the diameter midpoint formula can be used to find the center

Examples 10. center (1 , 4); point (3 , 4)

11. center (-1 , 2); point (-3 , 4)

12. endpoints of the diameter (1 , 6) and (5 , 9)

If an equation is not in standard form, we must complete the square to obtain standard form.  group like variables  move constants to the other side  complete the square for the x’s and y’s  take half of the “b” term, square it and add to both sides (do once for x and once for y)  factor the trinomial for the x’s and y’s

Examples Write the equation in standard form. Then state the center and the radius. 13. 14.