10.7 Equations of Circles

Which of the following is the equation of the circle with center: (5, -13) and radius: 11?

• $\left(x+5\right)^2+\left(y-13\right)^2=11$

• $\left(x-5\right)^2+\left(y+13\right)^2=11$

• $\left(x+5\right)^2+\left(y-13\right)^2=121$

• $\left(x-5\right)^2+\left(y+13\right)^2=121$

Which of the following is the equation of the circle with center: (-8, 0) and diameter: 5?

•  $\left(x-8\right)^2+y^2=6.25$ 

•  $\left(x+8\right)^2+y^2=6.25$ 

•  $\left(x-8\right)^2+y^2=25$ 

•  $\left(x+8\right)^2+y^2=25$ 

Which of the following is the equation of the circle with center: (12, -1) and radius:  $\sqrt{209}$  ?

•  $\left(x-12\right)^2+\left(y+1\right)^2=\sqrt{209}$ 

•  $\left(x+12\right)^2+\left(y-1\right)^2=\sqrt{209}$ 

•  $\left(x-12\right)^2+\left(y+1\right)^2=209$ 

•  $\left(x+12\right)^2+\left(y-1\right)^2=209$ 

What is the equation of this circle?

• (x + 3)² + (y - 1)² = 9
• (x - 3)² + (y + 1)² = 9
• (x - 3)² + (y + 1)² = 3
• (x + 3)² + (y - 1)² = 3

Tags

CCSS.HSG.GPE.A.1

Multiple Select: Choose all of the statements which are true for the equation:

(x - 4)² + (y - 3)² = 25 ?

• Center is at (4, 3)

• Radius of the circle is length 25

• Diameter of the circle is length 10

• Circumference of the circle is 50π

• Area of the circle is 25π

Multiple Select: Choose all of the statements which are true for the equation:

x² + (y - 6)² = 90.25 ?

• Center is at (0, -6)

• Radius of the circle is length 9.5

• Diameter of the circle is length 90.25

• Circumference of the circle is 19π

• Area of the circle is 90.25π

Which of the following is the equation of the circle with center: (10, 7) and circumference:  $14\pi$  ?

•  $\left(x+10\right)^2+\left(y+7\right)^2=7$ 

•  $\left(x+10\right)^2+\left(y+7\right)^2=49$ 

•  $\left(x-10\right)^2+\left(y-7\right)^2=7$ 

•  $\left(x-10\right)^2+\left(y-7\right)^2=49$ 

Which of the following is the equation of the circle with center: (-6, 2) and area:  $\pi$  ?

•  $\left(x+6\right)^2+\left(y-2\right)^2=0.25$ 

•  $\left(x+6\right)^2+\left(y-2\right)^2=1$ 

•  $\left(x-6\right)^2+\left(y+2\right)^2=0.25$ 

•  $\left(x-6\right)^2+\left(y+2\right)^2=1$ 

Which of the following is the equation of the circle with center: (-9, -3) and point on circle: (-11, 2) ?

•  $\left(x-9\right)^2+\left(y-3\right)^2=\sqrt{29}$ 

•  $\left(x-9\right)^2+\left(y-3\right)^2=29$ 

•  $\left(x+9\right)^2+\left(y+3\right)^2=\sqrt{29}$ 

•  $\left(x+9\right)^2+\left(y+3\right)^2=29$ 

Which of the following is the equation of the circle with endpoints of the diameter: (-8, 12) and (0, 2) ?

•  $\left(x+8\right)^2+\left(y-12\right)^2=164$ 

•  $\left(x+8\right)^2+\left(y-12\right)^2=\sqrt{164}$ 

•  $\left(x+4\right)^2+\left(y-7\right)^2=41$ 

•  $\left(x+4\right)^2+\left(y-7\right)^2=\sqrt{41}$