Question

If the equation of a conic section is `(x-2)^2+(y+5)^2=25`, how has its center been translated?

Answer 1

This is an equation of a circle. Note that all of the terms would have to be divided by 25 to put the relation is standard form. The standard form of this equation is ...

`(x-h)^2+(y-k)^2=1`, where `(h,k)` is the center of the circle.

You take the opposite sign of those values to find the center. In this example the center is `(2,-5)`.