College Algebra – Chapter 4 – Conic Sections - Circles

Circles:

• Definition: A ______________ is the set of all ___________ in a plane that are a fixed distance, called the _________________, from a fixed point, called the __________________.

• Standard Form:

_________________________________________________ o The vertex is the point (h, k) o The radius is the number r

r is not a point. It is a distance.

Use the information given to write the equation of the following circles. 1. Center at (4, 2) with a radius of 6.

2. Center at (-2, 3) with a radius of 32 .

Put the following equations into standard form. 3. x2 + y2 + 10x – 4y + 20 = 0

College Algebra – Chapter 4 – Conic Sections - Circles

4. 3x2 + 3y2 - 6x + 24y + 24 = 0 5. x2 + y2 + 14x + 45 = 0 6. 8! + !! − 2! = 64 − !! 7. !! + !!! + 14! − 12! + 4 = 0 8. !! + 2! + !! = 55 + 10! 9. 137 + 6! = !−!! − !!! − 24! 10. 8! + 32! + !! = !−263 − !!

College Algebra – Chapter 4 – Conic Sections - Circles

Put the following equations in standard form and graph the circle.

1. 364 + 28! + !! + !! = !−26! vertex: ___________ radius: ___________

2. −6! = −264 + 32! − !! − !! vertex: ___________ radius: ___________

College Algebra – Chapter 4 – Conic Sections - Circles

3. !! + !! + 24! + 10! + 160 = 0 vertex: ___________ radius: ___________

π4. 364 + 28! + !! + !! = !−26!

vertex: ___________ radius: ___________