Question

for the equation x² + y² - 4x - 8y - 16 = 0, do the following. (a) find the center (h,k) and radius r of the circle. (b) graph the circle. (c) find the intercepts, if any. (a) the center is (type an ordered pair.)

Explanation:

Step1: Rewrite the equation in standard form

The general equation of a circle is $(x - h)^2+(y - k)^2=r^2$. Given $x^{2}+y^{2}-4x - 8y-16 = 0$. Complete the square for $x$ and $y$ terms.
For the $x$ - terms: $x^{2}-4x=(x - 2)^{2}-4$.
For the $y$ - terms: $y^{2}-8y=(y - 4)^{2}-16$.
So the equation becomes $(x - 2)^{2}-4+(y - 4)^{2}-16-16 = 0$.

Step2: Simplify the equation

$(x - 2)^{2}+(y - 4)^{2}=36$.

Answer:

$(2,4)$