Question

i am seriously frustrated with this problem someone help me solve:
find the center and radius of each circle.
2x^2+2Y^2+14x+6y+2=0

Answer 1

First divide each term by 2

Answer 2

\[x^2+7x+y^2+3y+1=0\]

Answer 3

One-half of 7 is 7/2 and 7/2 squared is 49/4 so add 49/4 to both sides of the equation. (Also get the one over to the right side.)

Answer 4

\[x^2+7x+\frac{49}{4}+y^2+3y=-1+\frac{49}{4}\]

Answer 5

Now do the same thing with the 3y. One-half of 3 is 3/2 and 3/2 squared is 9/4 so add 9/4 to both sides.

Answer 6

\[x^2+7x+\frac{49}{4}+y^2+3y+\frac{9}{4}=-1+\frac{49}{4}+\frac{9}{4}\]

Answer 7

Now factor the left side and add the numbers on the right side together.

Answer 8

\[(x+\frac{7}{2})^2+(y+\frac{3}{2})^2=\frac{27}{2}\]

Answer 9

thanks i had everything but the right of the = sign correct I didnt divide the 2 from the original equation thanks

Answer 10

yw