SOLUTION: A and B are the points of intersection of the circle with equation x^2 + y^2 + 4x - 6y + 9 =0 and the diameter passing through origin. Find the coordinates of A and B.

Question 768566: A and B are the points of intersection of the circle with equation x^2 + y^2 + 4x - 6y + 9 =0 and the diameter passing through origin. Find the coordinates of A and B.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A and B are the points of intersection of the circle with equation x^2 + y^2 + 4x - 6y + 9 =0 and the diameter passing through origin. Find the coordinates of A and B.
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Find the center and radius of the circle.
x^2 + y^2 + 4x - 6y + 9 =0
x^2 + y^2 + 4x - 6y = -9

Center at (-2,3), r = 2
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Equation of the line thru the center and the Origin is
y = -3x/2
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Sub for y in the eqn of the circle.
x^2 + y^2 + 4x - 6y + 9 = 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=52 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.890599607549542, -3.10940039245046. Here's your graph:

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Use y = -3x/2 to find the y's of A and B

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