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Problem 76 Hard Difficulty

Find equations of both the tangent lines to the ellipse $ x^2 + 4y^2 = 36 $ that pass through the point (12, 3).

Answer

$$
y=3, y=\frac{2}{3} x-5
$$

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Video Transcript

this problem were given any question of Penelope's, and we're trying to find a question of times that Linda that's true for him. And three. Now we know that any question in a question or a line will be why I'm on this point times I'm comes X one's ex, not where we know why not is free. The next note is tool. So let's find this slope and how are we gonna find it? We're gonna take derivatives hopeless or angel equation, which is X He had two X Plus eight. Why, that's what 0.0 from this, we see that then why plan will be begging to X over for wine. Now we do not know where about all this at this point is not all this function. So let's keep why prime this way? And let's just put the things we know and to be to the seaQuest points will be how a woman's three, the sick of the negative eggs over or why Times X minus 12. Promise the female by both sides, or why we see that or wife's great minds ofour physical tainted, X scraped X. It means that your wife scrape plus expert who beat up 12 exposed actual one? No, we got left aside. We have a West produced expert and look at the question of the Ellipse. Given we don't expect possible why? Skirt is 36 that should be a patrol from sex. Why don't be three. We from here on that? What is it? About three miles. Thanks. You know, whenever we see why in the original question of Penelope's, we're gonna pluck three months. Extend there were sold for to find the points us to that be half expect us four times three minus X squared is equal 36 So x scraped. Waas 36 months 24 x plus four X spread Music 36 +364 guests out. He had five. Expert minus 24 X is it zero promise We see that X Times five Thanks when it's ready for his ego zero So that X could be zero or ex Could be 24 over five when it zero, uh, using this one, we see that why is equal to three and using this question of the slope right here. So we're using this this aggression to distinguish one so using a question. When we see that slope with an zero. Don't have any question of the tension. Land will be wise. It's great. It will just be a horizontal line. That one excess 10.4 over five. We see that. Why? Will be negative. Nine sort. Well, yeah, Well, we need to know what sort of using a question. One with you. That this look will be 24 over 64 That is two or three. Using these, we can find the question of 10 split as Boise to x over three furnace.