Question

Rewrite the following equation of a circle in general form: (x-7)^2+(y+8)^2=64

Answer 1

(a) x² +y² -14x +16y +49 = 0

Explanation:

You want the equation (x -7)² +(y +8)² = 64 written in general form.

General form

In general form, the terms are written in lexicographical order of decreasing degree, and the right side of the equation is 0.

Application

We know the square of a binomial is ...

(a +b)² = a² +2ab +b²

so we can write down the squares of the binomials:

x² -14x +49 +y² +16x +64 = 64

Rearranging and subtracting 64 from both sides, we have ...

x² +y² -14x +16y +49 = 0