find the center and the radius 8x^2+32x+8y^2+40y=46

Answer 1

Complete the square on the x and y terms to get

$(x+2{)}^2+(y+5/2{)}^2=(46/8)+4+(25/4)$ = 16

Then the center is (-2,-5/2) and the radius is 4.

I intentionally omitted the steps in completing the square because of my prior experience with limitations of the current editor for math symbols. But here are some hints:

First divide the 8 out of the x terms and the y terms; this gives you the 46/8 in the second line above.

To complete the square in the x terms, you add 4 and in the y terms you add 25/4. You should now be able to follow the answer.

If you are still stuck, please send me a message and I will try to help further.