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Problem 27 Easy Difficulty

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$ x^2 - xy - y^2 = 1, (2, 1) $ (hyperbola)

Answer

$$y-1=\frac{3}{4}(x-2), \text { or } y=\frac{3}{4} x-\frac{1}{2}$$

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Video Transcript

theme this trouble has to use in the position to find the crystal from land that's given point to one's to Mr. We know that the question of friends of mine will be off for one one's enough times. They were dropped this fortune, every checkpoint extract times explains X note where one is, Why not? And two. That's not so. Let's buying Derek first, let's do a take derivative off all the terms. With respect, X B have two x minus second term on the left. Inside. We're going for a rule we have. Why was X times? Why prime minus two. Why? Why prime is zero from this, uh, be plucked given points. And we can like this one as or minus one plus two y prime minus two y prime is equal to zero. Promise. We see that the four white crime should be pay. And why prime physical Buble or all right, since nobody have why problem your leg up given point, We are ready to applying everything we know. And so we have y minus on music three or four times explains to from this time we see that the congressional pension line is up on three X over four four minus one. Hello