QUESTION 1
The given circle has equation:
[tex]x^2+y^2=16[/tex]
We can rewrite to obtain;
[tex](x-0)^2+(y-0)^2=4^2[/tex]
This is equation is now in the form;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k)=(0,0) is the center of the circle and [tex]r=4[/tex] is the radius.
QUESTION 2
The center of the circle is at (1,1) and passes through the point (4,5).
The radius of this circle is given by;
[tex]r=\sqrt{(4-1)^2+(5-1)^2}[/tex]
[tex]r=\sqrt{(3)^2+(4)^2}[/tex]
[tex]r=\sqrt{9+16}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5[/tex] units.
We substitute into the formula;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x-1)^2+(y-1)^2=5^2[/tex]
[tex](x-1)^2+(y-1)^2=25[/tex]
Expand if you wish;
[tex]x^2-2x+1+y^2-2y+1=25[/tex]
[tex]x^2+y^2-2x-2y+2-25=0[/tex]
[tex]x^2+y^2-2x-2y-23=0[/tex]
