@Shaks
I'm hoping you understand the process of completing the square. We'll need that to get x2 + y2 + 4y + 2 = 0 into the standard form of the equation of a circle.
That standard form is (x - h) ^2 + (y - k) ^2 = r^2 where (h,k) are the coordinates of the center of the circle and r is the radius of the circle. Check out the attachment.
So, x^2 + y^2 + 4y + 2 = 0 can be written as x^2 + y^2 + 4y + __4_ = 0 + 4
(x + 0) ^2 + (y + 2) ^2 = 4 ---> Your Circle
Now, look at the standard form for the circle equation, compare it to the equation, and pick out the coordinates of the center and the value of the radius.
Post what you get, and I'll check. @Shaks
Look at standard form for circle equation:
That standard form is (x - h) ^2 + (y - k) ^2 = r^2 where (h,k) are the coordinates of the center of the circle and r is the radius of the circle.
What positive number times itself = 4? That's your r.
@Shaks I messed up by dropping the 2.
So, x^2 + y^2 + 4y + 2 = 0 can be written as x^2 + y^2 + 4y + __4_ = 2 + 4 = 6.
r^2 = 6 and r is square root of 6.
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
x + 42
= x