Answer:
[tex](x-4)^2+(y-7)^2=125[/tex]
Step-by-step explanation:
1) Find the radius
To find the radius of the circle, use the distance formula for the points (4,7) and (-7,9)
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the points (4,7) and (-7,9)
[tex]d=\sqrt{(-7-4)^2+(9-7)^2}\\d=\sqrt{(-11)^2+(2)^2}\\d=\sqrt{121+4}\\d=\sqrt{125}[/tex]
Therefore, the radius of the circle is [tex]\sqrt{125}[/tex] units.
2) Plug all data into the circle equation
Equation of a circle (not centred at the origin):
[tex](x-h)^2+(y-k)^2=r^2[/tex] where the centre is [tex](h,k)[/tex]
Plug in the point (4,7) as (h,k)
[tex](x-4)^2+(y-7)^2=r^2[/tex]
Plug in the radius [tex]\sqrt{125}[/tex]
[tex](x-4)^2+(y-7)^2=(\sqrt{125}) ^2\\(x-4)^2+(y-7)^2=125[/tex]
I hope this helps!
