Answer:
[tex](x-4)^2+(y+3)^2=20[/tex]
Step-by-step explanation:
The equation of a circle with center [tex](h,k)[/tex] and radius [tex]r[/tex] is given by [tex](x-h)^2+(y-k)^2=r^2[/tex].
What we know:
- Center at [tex](4,-3)[/tex]
To find the radius, we can use the distance formula. For points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex], the distance between them is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Let
[tex](x_1,y_1)\implies (-4, -3),\\(x_2,y_2)\implies (8,-1)[/tex]
[tex]r=\sqrt{(8-4)^2+(-1-(-3))^2},\\r=\sqrt{4^2+2^2},\\r=\sqrt{20}=2\sqrt{5}[/tex]
Thus, the equation of this circle is
[tex](x-4)^2+(y-(-3))^2=\sqrt{20}^2,\\\boxed{(x-4)^2+(y+3)^2=20}[/tex]
