Circle Equation Points on the Circle

A circle has a center at $\left(4,\ -1\right)$ and a radius of 6. Select all of the following that are points on the same circle.

A circle has a center at (1, 1). The diameter is 6. Which of the following points is a point on the circle?

A circle has diameter endpoints of (1, 0) and (5, 0). Which of the following points is a point on the same circle?

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

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

The equation of a circle is derived from

• gradient-intercept forumla

• point-slop form

• distance formula

• quadratic equation

What is the equation of the circle with the given information?

• A

• B

• C

• D

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.