Question

What is the equation of the circle with center (5,-4) and containing the points (5,-2)

Answer 1

The equation of a circle is
`(x-5)^2+(y+4)^2=4` .

Explanation:

-The equation of a circle is:

`(x-h)^2+(y-k)^2=r^2` (where center is
`(h,k)`, the point
`(x_(1),y_(1))` and the radius known as
`r`).

-Use the center (5,-4) and the point (5,-2) for the equation:

`(5-5)^2+(-2+4)^2=r^2`

-Solve the equation:

`(5-5)^2+(-2+4)^2=r^2`

`0 + (-2)^2=r^2`

`4 = r^2`

`√(4) = √(r^2)`

`2 = r`

-After you found the radius, use the center (5, -4) and radius 2 to get the equation of a circle:

`(x-5)^2+(y+4)^2=2^2`

-Then, after you have the equation, the radius needs to simplified by the exponent:

`(x-5)^2+(y+4)^2=4`