The equation of a circle is:
(x - h)² + (y - k)² = radius²
where (h, k) is the center.
We can plug in the given information from the description and solve for the radius.
(x - 2)² + (y - 4)² = radius²
To find the radius, we do the distance formula from the center to the point on the circle.
Distance = [tex] \sqrt{ (Y2-Y1)^{2} + (X2 - X1)^{2} } [/tex]
D = [tex] \sqrt{ (9 - 4)^{2} + (5 - 2)^{2} } [/tex]
D = [tex] \sqrt{ 5^{2} + 3^{2} } [/tex]
D = [tex] \sqrt{25 + 9} [/tex]
D = [tex] \sqrt{34} [/tex]
That is your radius. Now we plug it in.
(x - 2)² + (y - 4)² = (√34)²
Your final answer is:
(x - 2)² + (y - 4)² = 34
