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.
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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
{{{(x+2)^2 + (y-3)^2 = 4}}}
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
{{{x^2 + (9x^2)/4 + 4x + 9x + 9 = 0}}}
{{{13x^2/4 + 13x + 9 = 0}}}
*[invoke solve_quadratic_equation 3.25,13,9]
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{{{x = -2 +-sqrt(208)/13}}}
Use y = -3x/2 to find the y's of A and B