SOLUTION: For the given circle, find the x-intercepts and the y-intercepts. x^2+y^2-10x+4y+13=0 This is what I have so far: To find the x-intercepts let y=0 X^2-10x+13=0 (x+___)

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Question 288447: For the given circle, find the x-intercepts and the y-intercepts.
x^2+y^2-10x+4y+13=0
This is what I have so far:
To find the x-intercepts let y=0
X^2-10x+13=0
(x+___)(x-___) but this equation doesn't factor into integers as 13 is a prime number

Found 2 solutions by richwmiller, Alan3354:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
This circle crosses the x axis twice but never crosses the y axis at all.
You have to complete the square twice to find the center and radius. The y intercepts are not integers either.
The center is at integer points and the radius is an integer.
But the problem doesn't ask for those.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
For the given circle, find the x-intercepts and the y-intercepts.
x^2+y^2-10x+4y+13=0
This is what I have so far:
To find the x-intercepts let y=0
X^2-10x+13=0
this equation doesn't factor into integers as 13 is a prime number
Most of life is not integers.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=48 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8.46410161513775, 1.53589838486225. Here's your graph:


-----------------------
The x-intercepts are not integers.
------------
To get the y-intercepts:
y^2 + 4y + 13 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -36 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -36 is + or - .

The solution is , or
Here's your graph:

----------------
There are no real numbers solutions --> no y-intercepts.
--------------
If you complete the square:
x^2+y^2-10x+4y= -13
x^2-10x+25 + y^2+4y+4 = 16

The center of the circle is (5,-2) and its radius is 4.
It's 5 units to the right with a radius of 4, --> no y-intercepts.

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