Write the standard equation for the circle 30. Center (2,7), r=4. 31. Center (-6,-8), that passes treough (0,0)

The standard equation of the circle is:

(x-h) ^2 + (y-k) ^2=r^2 where (h, k) it the center of the circle and r is the radius ...

so

30.

(x-2) ^2 + (y-7) ^2=16

31.

We need to find the radius ... (I'll just use the Pythagorean Theorem)

r^2=6^2+8^2

r^2=36+64

r^2=100 (so the radius is 10) and its center is (-6,-8) so

(x+6) ^2 + (y+8) ^2=100