SOLUTION: Find the coordinates of the points of intersection of the line with equation y=kx+1 and the circle with equation x^2+y^2=9

Question 1029175: Find the coordinates of the points of intersection of the line with equation y=kx+1 and the circle with equation x^2+y^2=9
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the coordinates of the points of intersection of the line with equation y=kx+1 and the circle with equation x^2+y^2=9
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x^2+y^2=9
Sub for y
x^2 + (kx+1)^2 = 9
(k^2 + 1)x^2 + 2kx - 8 = 0
x = -2k/(k^2+1) + sqrt(4k^2 + 32k^2 + 32)/(2k^2 + 2)
x = (-2k + sqrt(k^2 + 8k^2 + 8))/(k^2 + 1)
y = k*(-2k + sqrt(k^2 + 8k^2 + 8))/(k^2 + 1) + 1 is one point.
and
x = (-2k - sqrt(k^2 + 8k^2 + 8))/(k^2 + 1)
y = k*(-2k - sqrt(k^2 + 8k^2 + 8))/(k^2 + 1) + 1 is another point.
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