Question

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

Answer 1

Step-by-step 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=√(100) \\ \\ h=-9,k=+6,r=10 \end{gathered}`

Therefore;

ANSWER:

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