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November 16th, 2012, 04:09 PM  #1 
Newbie Joined: Sep 2012 Posts: 3 Thanks: 0  Finding tangent lines on a curve through a point
Hi guys can you please help me out with this question: Find tangent lines on the curve x^2+4y^2=36 which pass through the point (12,3).

November 17th, 2012, 07:39 AM  #2 
Senior Member Joined: May 2011 Posts: 501 Thanks: 6  Re: Finding tangent lines on a curve through a point
This can be done implicitly, but another way is to solve the given for y. ............[1] The line that passes through (12,3) will be tangent to the lower half of the circle, The derivative is We can use and solve for x. Solving this for x may prove daunting, but we get Plugging this back results in So, one line is tangent at For the top portion, we use the positive case of [1] and get As I saod, this can be done implicitly by noting the slope is 

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curve, finding, lines, point, tangent 
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