Question

question 7, 2.4.29 part 2 of 4 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 (2,4). (type an ordered pair.) the radius is r =

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 to get the standard - form

$(x - 2)^{2}+(y - 4)^{2}=4 + 16+16$.
$(x - 2)^{2}+(y - 4)^{2}=36$.

Step3: Identify the radius

Comparing with the standard form $(x - h)^{2}+(y - k)^{2}=r^{2}$, where $r^{2}=36$, so $r = 6$.

Answer:

$6$