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December 17th, 2009, 12:45 AM   #1
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Find intersection of a Circle with Y-axis...

Please find the equation of circle, C1:
x2 + y2 + 4 x - 6y - 3 = 0
It has centre (-2,3) & Radius = 4

Hence, I need to find the intersection of the circle with Y-axis in 2 points A and B
Then to find the point D of intersection of the tangent line to the circle @ A and B

Thank you in Advance
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December 17th, 2009, 03:29 AM   #2
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Re: Find intersection of a Circle with Y-axis...

Answered elsewhere
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December 18th, 2009, 01:51 PM   #3
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Re: Find intersection of a Circle with Y-axis...

In this problem, the intersection with the axis Oy, is found by using itīs equation (Oy): x=0.
Solving the system defined by both equations will give you the points A(0,a) and B(0,b),
a and b will be the solutions to y2-6y-3=0.

At this time, you can also calculate the tangents on both of these points, but their intersection should be at y=3, can you see why?

Solving the equation y = (6 +-sqr(6*6-4(-3))/2= 3 +- sqr48/2= 3 +- sqr12 = 3 +-2sqr3
Then a = 3+2sqr3 and b = 3-2sqr3.
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