My Math Forum Find intersection of a Circle with Y-axis...

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 December 16th, 2009, 11:45 PM #1 Newbie   Joined: Dec 2009 Posts: 3 Thanks: 0 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
 December 17th, 2009, 02:29 AM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Find intersection of a Circle with Y-axis... Answered elsewhere http://www.sosmath.com/CBB/viewtopic.php?t=47866
 December 18th, 2009, 12:51 PM #3 Newbie   Joined: Dec 2009 Posts: 7 Thanks: 0 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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# interception of the x and y axis of a circle

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