find-an-equation-of-the-tangent-line-to-the-parabola-at-the-given-point-x22-yleft-3-frac22right

Question

Find an equation of the tangent line to the parabola at the given point.
$$x^{2}=2 y,\left(-3, \frac{2}{2}\right)$$

Ankit Gupta · Accepted Answer

we have been given the question off parabola access quite is quick trip away and we have to find the question off Poignant at the point minus three comma Mind by for that what will first, eventually. Okay, differential it With respect to ex Hogan, so do those two X. Everybody do do a bit being a letter told do. However, the X my m as M is this loop I m is because toe X and for minus three common nine by two Look it have a look of M s minus three and the sloping minus tree. So to find the question of penchant for you people like my minus five If I am X minus Excellent here, X one is a close to minus three and vibrant close to nine right toe. So we&#x27;ll put the value of I minus nine by two. It goes to minus three x plus three African multiply by two. So it becomes to white minus nine because it goes to minus six explicitly and it comes up with the Y minus nine years ago. Store minus six x minus Katie. And finally, the value consorted with two y plus six x is equal to nothing but minus nine. Hence, this is the required a question off the engine

Ankit Gupta · Answer

we have been given the question of the parable axis cooled to minus two y squared. And we need to find the question off the canyon at minus two comma minus one for that will proceed by differentiating differentiating with respect to X to the question of this parable. So what we get, we get there is one question minus four white Well played by Do you ever dx okay and will note deliver the X buy em, which is this. Look. Finally it comes out to me. One is gusto minus four white and and Emily Good. Dennis minus one upon four white No, we leave this flow at point minus two comma minus one. So we put the value off white, or you will get it was a close to minus one upon four. Good. Minus one. It&#x27;s abuse. Well, you have m s one by force. Now we have got to slowly find the question off the light without question. Why? Minus way. But is it closed? Toe em X minus X one. And you know that X one? Why would there&#x27;s nothing but minus two minus one? Okay, because the line is passing through this point so we can like as y minus minus one. That is why plus one is because too one by four and experts to multiply before will get four y plus four. Is he Quest Express toe? And finally, the kind into question is four way is because two x minus. This is required a question off the blended.

Ankit Gupta · Answer

we haven&#x27;t given the ocean off parable of that is excess close to minus two y squared. And we need to find the question off. Tangent has a point minus eight common. So first, let us differentiate. Differentiate with respect to X to the question of the parabola. So you get one because two minus four, like, can&#x27;t do wait digs on. Let us to know that wherever the exes come back, and so from beyond what we can do with Connecticut minus one bite full weight is he question nothing but divide where the X but is he goes to and okay. And by putting the value as minus eight, common to in this particular question of aloof and has minus one bite. Okay, okay. So minus one by eight becomes the value of them. And we need to find the question off light so it will find, with the help of five minutes, five minutes, coast with him x minus. Excellent. And we conveyed that X one weapon is nothing but minus eight coma because this line is passing from this particular point. So it becomes why minus told, she&#x27;s a close to minus one by it. X plus eight by multiplying by eight on the both sides, we get eight by minus 16 is a coastal minus, X minus eight. And finally the tendon to cushion. Is it right? Is it questo eight minus accents. This becomes the question off the quiet dungeon.

Clarissa Noh · Answer

he had clear. So when you right here. So the tangent line at point. A bee has slope m equals D Y over DX access equal to a and the form of the equation we use is gonna be point slope, which is why minus B equals m times X minus a. So we have m, which is our derivative d over d x of two X cubed minus X square plus two when X is equal to one and this gives for so the line equation is why minus three is equal to four terms X minus one, which is equal to four x minus one.

Ankit Gupta · Answer

we have been doing the question of parabolas, that Texas quality to it. And we need to find the tangent line at this point for coming for. For that first, let us find do everyday X. So it becomes two weeks as a questo. Don&#x27;t do. I like the X differentiating both the site with respect to X. So it gives nothing. But let us right back. Do I? Where the X is nothing about the slopes were to return it, so be there. X is questo total will be cancelled and we know that we need to find it for point for comedy 44 commit. So the slow comes out to be nothing but four. No, you need to find the question off the tangent line so it will become perkiness white minus weapon. Is it closed em X minus X one and here X one is close to four. On my own is a questo It I will put the value so it becomes Y minus eight. Is it questo? Well, you have m s poor and it&#x27;s minus four. Hence it becomes y minus eight is because too for X minus 16. And finally it comes upto for ticks, and he did it minus survival. Close to four explained. That is the question off Bandon at four comma eight.

Will Erickson · Answer

either. In this problem, we are asked to find the equation of a tangent line, Uh, at the given point for this curve. So the curve given is X Y plus X squared y squared equals five and her point will be two comma one. So, as always, when we want the equation of a tangent line, we have the point. We&#x27;re gonna end up using point slope form. The point is done. We just need the slope, which means we will need the derivative. So let&#x27;s begin. We can see right away we&#x27;re going to need implicit differentiation since the wise are all mixed in with the exes. So let&#x27;s take the derivative of the left and of the right and see what we get unless we&#x27;ll need the product rule for both of these, since we have X times why they&#x27;re so that&#x27;s used. The product room, the derivative of X y is X times the derivative of y, which is why prime or one times why prime plus the derivative of X is just one. So the product rule says derivative is X squared times the derivative of y squared, which is to why, But then we need to multiply by. Why Prime? That&#x27;s half the product rule. And then plus the derivative of X squared is to x on times the second part, which is just what I squared. So we did there. We used product rule the first term and the product fool on the second term. Okay. And then for the right side, the derivative of five is just zero. So at this point, all we have to do is get the white prime isolated here. So let&#x27;s look to see we have that term has a y prime, and so does this third term. And so we will distract. That&#x27;s a tract all the terms that don&#x27;t have a y prime. So we will subtract this term, Which is why who also subtract this term should minus two x y square. We&#x27;ll do that from both sides, which gives us X y prime plus C two x squared y y prime on the left and on the rights. We just get those two terms be subtracted from the left. Okay, Now we are ready to factor out that why prime from the left? And once we do that, we are basically, uh, one step away. So why Prime ends up being once we divide by everything on the left this&#x27;ll fraction here. That&#x27;s why prime now all that&#x27;s left to d&#x27;oh is plug in to for X and one for Why, since we want the slope at that point. So really, what we&#x27;re interested in since our slope. But this tangent line is going to be the derivative specifically at the 0.2 comma one and let&#x27;s just see what happens that&#x27;s plugged into for X and one for why? So we get minus. Why is one just two times X is too. Why is one then on bottom access to exes to And why is one all right? So on top, you get negative one, my ass four And on bottom we get two. Plus it should be ate, it looks like which is negative five on top 10 on bottom. That reduces to negative 1/2 That&#x27;s our slope. And now that we have the slope, we can answer the question. So the equation of our tangent line Remember the point slope form? Why, minus the point of the value of our point we know is one equals slope. It is negative half was. Put that into the slope Times X minus. The X coordinate we know is too. So there&#x27;s the final answer. If you want to put it into slope intercept form, you certainly can. But the problem doesn&#x27;t specify you have to. So there&#x27;s our Tanja line that out.

Problem

Find an equation of the tangent line to the parab…

Problem 94 Hard Difficulty

Find an equation of the tangent line to the parabola at the given point.
$$x^{2}=2 y,\left(-3, \frac{2}{2}\right)$$

Answer

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