Spring 2021 Performance Final Unit 8 Practice

Write the equation of a circle with center (h,k) and radius r.

• x^2 + y^2 = r^2

• (x + h)^2 + (y + h)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x - h)^2 - (h - k)^2 = r

Answer explanation

This is the basic standard equation of a circle. This is on your Unit at a Glance written for you.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4

• 2

• 3

• 16

Answer explanation

Remember that this is the pretty version they gave you! The pretty version has the radius already calculated out. so $r^2=4$ , what is r? It is 2.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

Answer explanation

Remember...x matches x, minus matches minus, h matches 3. so h is positive 3. y matches y, minus matches minus, k matches 2, so k is positive 2. (h,k) = (3,2)

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9

• x² + (y -7)² = 9

• (x - 7)² + y² = 3

• x² + (y -7)² = 3

Answer explanation

Remember: They gave you h, k, and r. Plug it into your Standard Equation of a circle, that is your ugly version. Now make your pretty version by fixing double negatives, zeros and calculate the radius out.

What are the coordinates of the center and theradius of the circle with an equation:

(x + 7)² + (y - 6)² = 64 ?

• Centre (7,-6)

  Radius = 8 units

• Centre (-7,6)

  Radius = 64 units

• Centre (-7,6)

  Radius = 8 units

• Centre (7,-6)

  Radius = 64 units

Answer explanation

Remember: x matches x, minus doesn't match minus, so what happened? what did h have to be for them to get a positive? It must have been a double negative to get a positive! (x - -7) , so your h must have been -7! moving on.... y matches y, minus matches minus, k matches 6. so k=6. Center is ( -7,6). moving on... the radius is 8 because the radius has already been calculated out to be 64 so $8^2=64$

What is the center of the circle with equation x² + y² = 1?

• (1, 1)

• (0, 0)

• not enough information

Answer explanation

Remember: if the h and k disappear from your pretty version, then they were zeros.

Determine the equation of the circle in standard form: x² + y² + 6x - 12y + 20 = 0

• (x-3)² + (y+6)² = 25

• (x+3)² + (y-6)² = 25

• (x-3)² + (y+6)² = 45

• (x+3)² + (y-6)² = 5

Answer explanation

Remember: This is the EXPANDED FORM. You need to complete the square to put it in Standard form. This is on your Performance Final At-A-Glance.

What is the center and radius of the ANSWER you got in the last question?

• Center : (-3,6)

  radius = 5

• Center : (-3,6)

  radius = 25

• Center : (3,-6)

  radius = 5

• Center : (3,-6)

  radius = 25

Answer explanation

Remember: After you find the standard equation, you can grab the center and radius from the ugly version from it. The h, k, and r.