Question

THERE IS 2 PROBLEMS TOGETHER FOR A THIRD PROBLEM SO PLEASE ANSWER BOTH.Read image for instructions.

Answer 1

The Solution.

The given equation of a circle is

`(x-1)^2+(y-2)^2=16\ldots eqn(1)`

By formula, the equation of a circle is

`\begin{gathered} (x-a)^2+(y-b)^2=r^2\ldots eqn(2) \\ \text{where the center is (a,b), and r=radius} \end{gathered}`

Comparing the corresponding terms in eqn(1) and eqn(2), we have

`\begin{gathered} x-a=x-1 \\ \Rightarrow a=1 \end{gathered}`

Similarly,

`\begin{gathered} y-b=y-2 \\ \Rightarrow b=2 \end{gathered}`

Also,

`\begin{gathered} r^2=16 \\ r=\sqrt[]{16}=\pm4 \\ r=\text{ +4 units ( -4 is discarded)} \end{gathered}`

Hence, the center of the circle is (1,2) while the radius of the circle is 4 units.