Answer:
[tex]{(x + 3)}^{2} + {(y - 4)}^{2}=98[/tex]
Step-by-step explanation:
The standard form equation of a circle is given as:
[tex] {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]
Where (a,b) is the center and r is the radius.
We need to use the distance formula to obtain the radius.
[tex]r = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]
We substitute the center (-3,5) and (4,-2) to get:
[tex]r = \sqrt{(4- - 3)^2 +( - 2 - 5)^2} [/tex]
[tex]r = \sqrt{(7)^2 +( - 7)^2} [/tex]
[tex]r = \sqrt{98} [/tex]
We now substitute the center and radius to get:
[tex] {(x - - 3)}^{2} + {(y - 4)}^{2} = { (\sqrt{98} })^{2} [/tex]
The standard form equation is;
[tex]{(x + 3)}^{2} + {(y - 4)}^{2}=98[/tex]
