Answer:
[tex]\huge\boxed{(x-8) ^2+(y-2)^2=225}[/tex]
Useful information:
Equation of a circle:
[tex](x-h) ^2+(y-k)^2=r^2[/tex]
Distance formula:
[tex]r=\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1})^2[/tex]
Step-by-step explanation:
1) Find the centre of the circle
From the equation of a circle, the values of h and k represent the centre of the circle and r the radius. The first step is to identify the centre of the circle. From the question, we know that the centre is (h, k) in the equation of a circle, so (h, k) = (8, 2).
2) Find the radius.
The next step is to find the radius of the circle. The radius (r) is the distance from the centre to any point on the circle. We'll use the distance formula between (8, 2) and (17, 14) to find the radius by plugging in the coordinates.
[tex]r=\sqrt{(17-8)^2+(14-2)^2[/tex]
[tex]r=15[/tex]
3) Express in the equation of the circle.
Now that we have the center (h, k) = (8, 2) and the radius (r) = 15, we can write this information in the equation of a circle.
[tex](x-8) ^2+(y-2)^2=15^2[/tex]
[tex](x-8) ^2+(y-2)^2=225[/tex]
