Question

Identify the center and the radius then write the equation of the circle

Answer 1

Given

The circle,

To find the center, radius and the equation of the circle.

Step-by-step explanation:

It is given that,

From, the figure,

The center of the circle is (3,-1).

And, the radius of the circle is 4units.

Therefore, the equation of the circle is,

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-3)^2+(y-(-1))^2=4^2 \\ (x-3)^2+(y+1)^2=16 \\ x^2-6x+9+y^2+2y+1=16 \\ x^2+y^2-6x+2y+10-16=0 \\ x^2+y^2-6x+2y-6=0 \end{gathered}`

Hence, the center of the circle is (3,-1), the radius is 4units, and the equation of the circle is x²+y²-6x+2y-6=0.