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