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  $(h,k)=(13.40,-2.60)\\r=10$ .

Step-by-step 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 $(h,k)=(13.40,-2.60)\\r=10$ .