Answer:
[tex](x - 4)^{2} + (y - 3)^{2} = 53[/tex]
Step-by-step explanation:
The general equation of a circle is as follows:
[tex](x - x_{c})^{2} + (y - y_{c})^{2} = r^{2}[/tex]
In which the center is [tex](x_{c}, y_{c})[/tex], and r is the radius.
In this problem, we have that:
[tex]x_{c} = 4, y_{c} = 3[/tex]
So
[tex](x - 4)^{2} + (y - 3)^{2} = r^{2}[/tex]
Passing through (2,-4)
We replace into the equation to find the radius.
[tex](2 - 4)^{2} + (-4 - 3)^{2} = r^{2}[/tex]
[tex]4 + 49 = r^{2}[/tex]
[tex]r^{2} = 53[/tex]
The equation of the circle is:
[tex](x - 4)^{2} + (y - 3)^{2} = 53[/tex]
