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Problem 31 Easy Difficulty

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
$ 2(x^2 + y^2)^2 = 25(x^2 - y^2), (3, 1), $ (lemniscate)

Answer

$$y-1=-\frac{9}{13}(x-3) \text { or } y=-\frac{9}{13} x+\frac{40}{13}$$

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Video Transcript

in this problem we asked to use in visit differentiation to find the question of mine to be given occur at this given going free. Or you know that Krishna country level B Y minus Warner is equal to their return. You let that given points Times X minus. Not so. Let's first find Trevor to hope dysfunction Elect in point. Spread out. Let's first derivative or both sides suspect X. We have four times Express bus. Why spread what's fight by their report in your function, which is two eggs? What's to why Times y prime is equal to 25. Just bouncing times two x minus two Why time, Time. All right, we know what X nuts and why are so. We can just point those in to find every two able that's given points. Let's do that. You have four times 10 times six plus two are prime is equal to 25 times six months to work from. Wife is coming, sort of the five of the two we end up with 48 waas. 16 were prime physical, 30 minus 10 more prime. From this, we find what crime to be negative. Nine. Forward for team. And if you play that in, uh, just given potential any question we find time to let to be minus one is equal to negative. Nine over 13. Ex wants free. From this, we find the question to be that wise. A coordinated night X over 13 plus 40 over 13. All right.