Question

Conics: Write in standard form
4x^2+4y^2+32x-18y+37=0

Answer 1

its a circle!
so we need to put in the form
(x-h)^2+(y-k)^2=r^2

Answer 2

Complete the square for x and y.

Answer 3

For completing the square I was confused because of the 7 you get when you factor the 4 out for y

Answer 4

divide everything by 4
\[x^2+y^2+8x-\frac{9}{2}y+\frac{37}{4}=0\]

Answer 5

\[x^2+8x+(\frac{8}{2})^2+y^2-\frac{9}{2}y+(\frac{9}{2*2})^2+\frac{37}{4}=16+\frac{81}{16}\]

Answer 6

\[(x+4)^2+(y-\frac{9}{4})^2=\frac{337}{16}\]

Answer 7

So if I am also looking for the center and radius it would be
-4, \[(9 \ 4)\] and the radius would be \[\sqrt{337/16}\] ?

Answer 8

*-4, (9/4)

Answer 9

yep

Answer 10

Thank you so much

Answer 11

Thank you so much