can some one help me with this algebra 2 prob?

Question

cosider x squared + 10 x + y squared=0 find the center and radius and sketch the graph?

Answer 1

x^2 + 10x + y^2 = 0

Complete the square for x

x^2 + 10x + 25 + y^2 = 25
(x + 5)^2 + (y-0)^2 = 5^2

A circle centered at (-5, 0) with radius 5.

Answer 2

Just to reiterate your question using more common notation on answers: x^2 + 10x + y^2 = 0

The general form of a circle is as follows;

(x-h)^2 + (y - k)^2 = r^2, with the coordinates of the center being (h,k) [note: you take the NEGATIVE of how h and k appear in the equation] and r being the radius.

In order to determine the center and radius of the above graph, i.e.

x^2 + 10x + y^2 = 0

You have to complete the square for the x terms. The term that would complete the square is 25, so you have to add 25 to the right hand side as well.

x^2 + 10x + 25 + y^2 = 0 + 25
(x+5)^2 + y^2 = 25

Thus, you now know the x-coordinate of the center; it's -5 (since the 5 in brackets is positive, and we take the negative of it). The y-coordinate of the center isn't immediately obvious, but note that
y^2 = (y+0)^2, so 0 is the y-coordinate of the center.

So the coordinates of the center are (-5,0).

To get the radius, you must consider that r^2 = 25 (i.e. the right hand side is supposed to contain the radius squared), so we just take the positive square root and find that r = 5. We discard the negative square root for this case because radii must be positive.

Therefore, to sketch the graph, you must first locate the point (-5,0), make a dot 5 points to the right, then make a dot 5 points up, then make a dot 5 points left, then make a dot 5 points down, and connect them to form a circle.

Answer 3

(x+5)^2+(y)^2=25
center(-5,0)
radius=5 units
itis a circle