Question

The equation of a circle is given below.

(2 – 13.4)2 + (y + 2.6)2 = 100
What is its center?
What is its radius?
If necessary, round your answer to two decimal places.
units
Help

Answer 1

Coordinates of center and radius of circle is
`(h,k)=(13.40,-2.60)\\r=10` .

Explanation:

Here we have , The equation of a circle is given below.

(2 – 13.4)2 + (y + 2.6)2 = 100 or ,
`(x -13.4)^2 + (y + 2.6)^2 = 100`

We know that , Equation of circle is given by :

⇒
`(x-h)^+(y-k)^2 =r^2` ...........(1)

where (h,k) are the coordinates of center of circle and r is the radius of circle . Let's simplify given equation of circle in question ;

⇒
`(x -13.4)^2 + (y + 2.6)^2 = 100`

⇒
`(x -(13.4))^2 + (y - (-2.6))^2 = 100`

⇒
`(x -(13.4))^2 + (y - (-2.6))^2 = 10^2`

Comparing this equation to (1) we get :

`(h,k)=(13.40,-2.60)\\r=10`

Therefore , Coordinates of center and radius of circle is
`(h,k)=(13.40,-2.60)\\r=10` .