Question

The general form of the equation of a circle is x2+y2−4x−8y−5=0. What are the coordinates of the center of the circle?

Answer 1

The center of the circle is at `(2,4)` and the circle has a radius of `5`.

Explanation:

Formatted question: `x^2+y^2-4x-8y-5=0`

Note: The standard form a circle is `(x-h)^2+(y-k)^2=r^2`, where `(h,k)` is the center of the circle and `r` is the radius of the circle.

To find the standard form of the circle, we need to complete the square and move the constants to the right side:
`x^2+y^2-4x-8y=5`
`(x-2)^2-4+(y-4)^2-16=5`
`(x-2)^2+(y-4)^2=25`

Therefore, the center of the circle is at `(2,4)` and the circle has a radius of `5`.