💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 44 Hard Difficulty

Show by implicit differentiation that the ellipse
$ \frac {x^2}{a^2} + \frac {y^2}{b^2} = 1 $
at the point $ ( x_o, y_o) $ is
$ \frac {x_o x}{a^2} + \frac {y_o y}{b^2} = 1 $



More Answers


You must be signed in to discuss.

Video Transcript

in this problem were given any question of Penelope's and whereas to show that at Point X not one on congressional attention Fine as this given equation. All right, you know, the question of the kinds of line is up for one minus one up is they're a joke dysfunction. It will look at Devon Point times. That's one that's not so. We need to find a withdrawal. This bunch. Let's differentiate given question. We have to. That's or a square was, too. I over b Square 10 white crime Is it One l s black. Be given up once and we have two times. It's not over a squared plus two times Why not over b squared times y prime physical boot polish. Zero sense is Alison. This is zero from this time we see that why crime is evil. Lay ahead of me. Screw or be screwed Times X note bore. Why no where? All right now, if that is what crime we can write the question of times like ISS. Why minus point out is a quick negative be scraped or h fire times X note over. Why not both fight by experts ex not less. Divide bolts less month by both sides by age three times Watch spray. This would give us a square. Why not times Y minus space grade? Why not squared is equal to native B squared x not times X plus B squared times Excellent for all right? Yeah, we can let this one as a squared times. Why not four plus B squared times Excellent times X is equal to Ace grade boy. A squared plus B squared extent screwed. Let's month find both sides or less to my boat size by one or a spirit comes eastward Be would end up with 19 times one or be spread Waas exploit times X behind a sward physical too. Why not spurt over? Be spread plus X not spared over a spurt. Now look at the writing side we have here and look at the orginal question. If you put ex nun and one up into the sea question we would get the right hand side. Right. So we know that this right hand side is he won so that we end up with Why not? Over y off piece for us. X, not X over expert physical one. As you can see, that is actually a question off the tension. What? Oh