Step 1
State the equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h= -7
k= 7
Step 2
Find r
r is the distance between the origin and (-7,7)
Distance between 2 points is
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}}[/tex][tex]\begin{gathered} \text{where} \\ x_2=0 \\ x_1=-7 \\ y_2=0 \\ y_1=7 \end{gathered}[/tex]Hence the distance is given as
[tex]\begin{gathered} d=\sqrt[]{(0-(-7))^2+(0-7)^2} \\ d\text{ =}\sqrt[]{49+49} \\ d=\sqrt[]{98} \\ d=7\sqrt[]{2} \end{gathered}[/tex]Hence r =7√2
Step 3
Write the equation in standard form after substitution.
[tex]\begin{gathered} (x-(-7))^2+(y-7)^2=(7\sqrt[]{2})^2 \\ (x+7)^2+(y-7)^2=(7\sqrt[]{2})^2 \end{gathered}[/tex]