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November 16th, 2012, 04:09 PM   #1
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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).
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November 17th, 2012, 07:39 AM   #2
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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.


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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