SOLUTION: if a cirlce has (-2,-3) and (6,1) as endpoints of its diameter where does the circle cross the y-axis?

Question 435599: if a cirlce has (-2,-3) and (6,1) as endpoints of its diameter where does the circle cross the y-axis?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the eqn of the circle:
The midpoint is the center, point C
Cx = (-2+6)/2 = 2
Cy = (-3+1)/2 = -1
Center @ (2,-1)
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The radius is the distance from C to either point

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is the circle
It crosses the x-axis when y = 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 : .

Discriminant d=76 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.35889894354067, -2.35889894354067. Here's your graph:

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x = 2 +/- sqrt(19)

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