Question

The equation of a circle is (x + 9)*2 + (y - 6)*2 = 100. What is the radius and center of thecircle?

Answer 1

EXPLANATION:

Given;

We are given the equation of a circle as shown below;

$(x+9)^2+(y-6)^2=100$

Required;

We are required to use the information provided to calculate the radius and center of the circle.

Step-by-step solution;

The standard equation of a circle is given as follows;

$(x-h)^2+(y-k)^2=r^2$

Here, the variables are;

$\begin{gathered} (h,k)=center\text{ }of\text{ }the\text{ }circle \\ r=radius \end{gathered}$

Note that the equation provided here is already in standard form.

Therefore, we can observe the following;

$\begin{gathered} (x+9)^2+(y-6)^2=100 \\ For: \\ (x-h)^2+(y-k)^2=r^2 \\ We\text{ }have: \\ (x-[+9])^2+(y-[-6])^2=\sqrt{100} \\ \\ h=-9,k=+6,r=10 \end{gathered}$

Therefore;

ANSWER:

$\begin{gathered} Center=(-9,6) \\ Radius=10 \end{gathered}$