Deriving and using the equation of a circle

Find the center of the circle  $x^2-2x+y^2+10y+17=0$  

• (5,-1)

• (-5,1)

• (1,-5)

• (-1,5)

Is point A(-3 , 8) inside, outside or on the circle whose equation is given by

x ² + 4x + y ² - 8y = 5

• Inside the circle

• Outside the circle

• On the circle

Which is the equation of this circle?

• None of these

Change the following equation to standard form   $y^2+x^2+4x-16y+160=416$  

•  $\left(x+2\right)^2+\left(y-8\right)^2=324$  
  

•  $\left(x+2\right)^2+\left(y-8\right)^2=256$  
  

•  $\left(x-8\right)^2+\left(y+2\right)^2=324$  
  

•  $\left(x+8\right)^2+\left(y-2\right)^2=256$  
  

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

• (x+2)² + (y+3)² = 49
• (x+2)² + (y+3)² = 13
• (x-2)² + (y-3)² = 49
• (x-2)² + (y-3)² = 13

• 49

• 2401

• 98

• 7

The equation of a circle is given by  $x^2+y^2-6x+9y\ -18=0$ . What is the center and radius of the circle

• Center (3,-4.5) radius 6.9

• Center (3, -4.5) radius 7

• Center (-3, 4.5) radius 6.9

• Center (-3, 4.5) radius 47.25

Use the information provided to write the standard form equation of the circle.

• A

• B

• C

• D

Write the Equation to the circle with center of (2,5) and radius 6.

• (x-2)² + (y-5)²= 6

• (x-2)² + (y-5)²= 36

• (x+2)² + (y-5)²= 6

• (x+2)² + (y+5)²= 36

Which of the following points is INSIDE the circle that has the equation:

(x-3)² + (y+3)² = 25?

• (-2, -3)

• (3, 1)

• (0, 2)

• (-1, 2)