Problem

Show that the sum of the $ x- $ and $ y- $ interc…

02:37

Problem 45 Hard Difficulty

Find an equation of the tangent line to the hyperbola
$ \frac {x^2}{a^2} - \frac {y^2}{b^2} = 1 $
at the point $ (x_o, y_o). $

Answer

$$\frac{x_{0} x}{a^{2}}-\frac{y_{0} y}{b^{2}}=\frac{x_{0}^{2}}{a^{2}}-\frac{y_{0}^{2}}{b^{2}}=1$$

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Video Transcript

in this problem, we're going in question. And where s a final question of tension line that important? It's gonna Why not be known at the question of pencil and move you or y minus order Physical, too slow or David or dysfunction? It will get given point off if I explain it's Exner, for we first need to pack plate conservative industry point. So let's differentiate this given in question. We have to ex or a sprayed minus two r or B squared y prime Izzy zero from this. Then we see that what prime is equal to thanks over a spread times bees for a while or redirect this one as a virtually dissect given point. We would find why five to be equal to bees. Word over a scrape month like ex. Not we're going up that if that is, why primarily given. Let's write. Be questioned tangling again. We have one minus one is equal to be scared over a squared times X No, no. Why not? Well, like my ex months ex, not now. Let's multiply both sides by a straight times. Why not? Um, you would end up with a straight times wine up on four minus a spring times. Why not? Squared is equal to B squared X nine times, X minus B squared pig snouts crab we can write for do this One is a spurred by not time for minus be spared. Excellent X that is equal to be screwed. That is he going to piece Fred Ex not spread minus a spring. Why not? Square? All right. Um well, that should be the underwear up this b a screwed. Why not? Spread minus be spurred. Excellent spur or now it be. Divide both sides. Fine. A squared times be spurred. You would end up with eggs. Not Or why not? Times why divided a B squared minus extra funds exit the life by a spread is equal to why no, it's great. Be spread minus x Not spread you on a squared or this is Samos Exact times like so race bird minus one on time for lawyer will be spread is a question Excellent Squared away. Scrape plus or minus one up spread over these four. So basically I most vital signs are negative. Or now look at the right inside here and look at the origin of the question. Is he blinking point? Excellent order into the ordinary question. It would end up with one. And since right that side is the same, we're going to say that frightening side, is it? Well, so then the question of potential lead is excellent. Point X provide a sprig minus one for a while, but he's very busy.

Doruk I.

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Problem

Show that the sum of the $ x- $ and $ y- $ interc…

Problem 45 Hard Difficulty

Find an equation of the tangent line to the hyperbola
$ \frac {x^2}{a^2} - \frac {y^2}{b^2} = 1 $
at the point $ (x_o, y_o). $

Answer

$$\frac{x_{0} x}{a^{2}}-\frac{y_{0} y}{b^{2}}=\frac{x_{0}^{2}}{a^{2}}-\frac{y_{0}^{2}}{b^{2}}=1$$

More Answers

Related Courses

Calculus: Early Transcendentals

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