Question

Write the standard equation of the circle with center (4, -2) and radius 5.2.

Answer 1

If the radius is really 5.2, then the standard equation of this circle is:

`(x-4)^2+(y+2)^2=27.04`

Now, if there was a typo in your question, and the radius is "5", then, the equation becomes:

`(x-4)^2+(y+2)^2=25`

Explanation:

Recall that the standard equation for a circle of radius R, centered at
`(x_0,y_0)`, is given by:

`(x-x_0)^2+(y-y_0)^2=R^2`

Therefore in the case of a circle of radius R = 5.2, and centered at (4, -2), we have:

`(x-x_0)^2+(y-y_0)^2=R^2\\(x-4)^2+(y-(-2))^2=(5.2)^2\\(x-4)^2+(y+2)^2=27.04`