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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.

............[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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