Please help with calculus question regarding circles

Question

the equation for the general form of a circle is 2x² +8x +2y² -y -2 . I have done this problem countless times and cannot for the life of me get the radius. I have found h = -2 and k = 1/8. Can someone please show me how to get the radius.

Answer 1

2x² + 8x   +    2y² - y      =   2

 

2 (x² + 4x + 4)     + 2 (y² - y/2 + 1/16) = 2 + 8 + 1/8

 

2(x + 2)² + 2(y - 1/4)² = 81/8

 

(x + 2)² + (y - 1/4)² = 81/16

 

center is (-2, 1/4)

 

radius is 9/4

Answer 2

Anabel,

 

   What is one the other side of the first "equation?"

 

   If the last "-" is an "=" then,

 

2(x²+4x)+2(y²-y/2) = 2 by factoring.

 

Complete the square, to get

 

2(x²+4x+4)+2(y²-y/2+1/16) = 2 + 8 + 1/8

 

(x+2)²+(y-1/4)² = 81/16

Answer 3

2x²+8x+2y²-y-2 = 0

By dividing both sides  by 2, we got the following:

x²+4x+y²-(1/2)y-1 = 0

Moving the number to the other side gives the following equation:

x²+4x+y²-(1/2)y=1

Then, we need to complete the square for each x and y term, by adding number corresponding to the square of 1/2 of coefficient in front of x (or y).

(x²+4x+2²)+(y²-(1/2)y+(1/4)²=1+2²+(1/4)²

Which can be rearange to

(x+2)²+(y-1/4)²=(16+64+1)/16

                        = 81/16

Recall the circle equation: (x-h)²+(y-k)²=r². Therefore, center of circle (-1, 1/4) and radius = 9/4