Equations of a Circle Given Points

What is the equation for this circle?

• (x+1)²+(y+1)²=9

• x²+y²=9

• x²+y²=6

• x²+y²=3

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

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 2)² + (y + 5)² = 36

• (x - 5)² + (y + 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 6

What is the equation of the circle shown in the graph?

Mathematical Equivalence

ON

Find an equation of the circle whose center is at the point (-4 , 6) and passes through the point (1 , 2).

The endpoints of a diameter of a circle are (3,1) and (9,5). Find the equation of the circle.

• (x − 6)² + (y − 3)² = 13

• (x − 3)² + (y − 6)² = 169

• (x − 5)² + (y − 9)² = 13

• (x − 9)² + (y − 5)² = 42.25

Find the equation of the circle with center (−8,3) and (2,−5) is on the circle?

• (x+8)²+(y−3)²=164^.5.

• (x+3)²+(y−8)²=164.

• (x)²+(y)²=164.

• (x+8)²+(y−3)²=164.

A circle has a center of (1, -5) and passes through the point (-7, -13). What is the equation of this circle? (Hint: graph to find the length of the radius).

• (x + 1)² + (y - 5)² = 128

• (x - 1)² + (y + 5)² = 11.31

• (x - 1)² + (y + 5)² = 128

• (x + 1)² + (y + 5)² = 11.31

Find the equation of the circle with center (−8,3) and (2,−5) is on the circle?
Hint: you need to find the radius by plugging in values for four variables 
x=
y=
h=
k=
in (x-h)²+(y-k)²=r²

• (x+8)²+(y−3)²=164^.5.

• (x+3)²+(y−8)²=164.

• (x)²+(y)²=164.

• (x+8)²+(y−3)²=164.