Question

I need help with this I need to know what I’m doing wrong.. do I need to put a negative for (y+8^2) or a positive 8 so confused… help #4write in standard equation for a circle and identify center and radius

Answer 1

4) You have the following equation:

`x^2+10x+y^2-16=0`

In order to determine the radius and center of the circle, complete squares for x. You don't complete squares for y because there is no term with y in the given expression. It is only a y^2 term.

By adding 25 and subtracting 25 left side of the equation you obtain:

`x^2+10x+25+y^2-16-25=0`

The first three terms are a perfect square (x + 5)^2, then, by using this factor and by simplifying in the previous equation you can write:

`(x+5)^2+y^2-41=0`

Finally, add 41 both sides:

`(x+5)^2+y^2=41`

The previous equation is in standard form for a circle equation:

`(x-h)^2+(y-k)^2=r^2`

(h,k) is the center of the circle and r the radius. By comparin the previous equation with the expression you obtain you obtain:

center of the circle = (-5,0)

radius r = √41