Answer:
[tex]c) (x-h)^{2}+(y-v)^{2}=r^{2}[/tex]
Step-by-step explanation:
Hi There,
1. The Circle formula in its standard form is given by:
[tex](x-a)^{2}+(y-b)^{2}=r^{2}\Rightarrow C=(a,b)[/tex]
2) This coordinates a, b are the Center coordinates of the Center, a point distant from the circumference by the radius.
3) Because we can find derive this formula from that. (Check the graph below)
There's a point P(x,y) whose distance to C(h,v) is the radius, we need to calculate it numerically:
[tex]r=\sqrt{(x-h)^{2}+(y-v)^{2}} \:or\:r^{2}=(x-h)^{2}+(y-v)^{2}\\r=\sqrt{x^{2}-2hx+h^{2}+y^{2}+2vy+v^{2}}\\r=\sqrt{x^{2}+h^{2}+y^{2}+v^{2}}\\(r)^{2}=(\sqrt{x^{2}+h^{2}+y^{2}+v^{2}})^{2}\\r^{2}=x^{2}+h^{2}+y^{2}+v^{2}\\r^{2}=x^{2}+y^{2}+h^{2}+v^{2}\\\\[/tex]
4) Hence, as the Center has its coordinates C(h,v) then its circle formula is:
[tex]c) (x-h)^{2}+(y-v)^{2}=r^{2}[/tex]
