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IsTim
 2 years ago
Determine the equation of the tangent to the curve at a given point.
x^2+9y^2=37 (1,2)
IsTim
 2 years ago
Determine the equation of the tangent to the curve at a given point. x^2+9y^2=37 (1,2)

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IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I've gotten the slope of 1/18, but I don't know if that's correct. And if so, how do I continue?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0So, first, dy/dx=x/dy. I then subbed in (1,2) and got 1/18.

CHAD159753
 2 years ago
Best ResponseYou've already chosen the best response.0Lol uhh so I cant give answers so ill just leave now but what youv done so far is correct :D

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I don't need the answer. I need to know what my process afterwards should be.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1What's the derivative?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1And Chad is in 11th grade, he won't be able to help you

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.01. Derivative is 2x+18y(dy/dx)=0. Right? 2. I figured that out already...

CHAD159753
 2 years ago
Best ResponseYou've already chosen the best response.0lol ink I can give him an answer ;D

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1x^2+9y^2=37 dy/dx 37=dy/dx x^2+dy/dx 9y^2 0=2x+18y dy/dx

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1No, you won't give him the answer he's looking for. THe answer he's looking for is an explanation, because, as everyone knows, it's the explanantion that matters in calc

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I already have the answer in my textbook and potentially Wolfram Alpha. I need to know how to GET there though.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1Normally at this point I try to isolate dy/dx for convenience

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.10=2x+18y dy/dx (2x)/(18y)=dy/dx x/(9y)=dy/dx

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah, I think I did that.It's x/dy right? @ Shruti: I don't think so...

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1And, my answer agrees with your answer here.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1Although my work here is moot, because i'm in 9th grade.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. Thanks for the help so far.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. How would I get to the answer of x+18y37=0 from knowing that the slope is 1/18?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1If you had the derivative and wanted to get the original equation?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0@shruti By conics did you mean http://www.purplemath.com/modules/circle3.htm

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0since this is an equation of an ellipse, y can be considered an implicit function of x right?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I guess. My notes only reveal the steps. This work is not from a textbook.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0In fact, it's not even addressed in my textbook. That's strange.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0it can be .... to derive implicitly, ignore the form of the variable and treat everything as tho it acted like you normally think of deriving x^2+9y^2=37 ; just derive it all, but dont toss out the derived bits 2x x' + 18y y' = 0 now lets consider this when we derive it with respect to x x' = dx/dx = 1 y' = dy/dx like normal so, lets solve it for y'

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1If you have the derivative, and want to get the original equation, you take the antiderivative of it

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1If you're asking about taking antiderivatives (indefinite integrals), and have not yet learned about rieman sums, don't worry about the question

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1Otherwise, I might have to look into it.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Y' is x/dy, which, when we sub in (1,2) is 1/18 right?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0What would I do next then?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1Well, you have a point, and a slope.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1(1,2) > point 1/18 > slope

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Would I sub those into y=mx+b?

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.0you have slope, you have a point, put it in point slope form...

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1put in the point and the slope, and then you have b

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1then, put in y=mx+b, cept don't put in that point

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1This isn't a calculus problem, this is an algebra problem, :D

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, what is point slope form? It's algebra? I must really have been "dumbing" down these years...

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1There's multiple ways of writing the equation for a line.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1This is point slope: yy1=m(xx1)

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1this is slope intecept: y=mx+b

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1This is standard form: ax+by=c

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1I normally work with slope intercept, because i'm more used to it.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1However, point slope is the fastest way to go here.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1yy1=m(xx1) (x1,y1)=(1,2) m=1/18

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0The answer is in the form of ax+by=c I guess, but I am also more familiar with slope intercept.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, I already have the slope... I know it is 1/18. But how do I get to x+18y37?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1y1=(1/18)(x2) now, just isolate y, and distribute x

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1They have given you the point that the line must pass through, and you have found the slope,

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Oh. I finally understand. Thank you very much. I will call out again if I need help.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, 1 and 2 in y1=(1/18)(x2)/ Shouldn't it be y2=(1/18)(x1)? Because (1,2)?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1I got it confused myself. xD

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Why doesn't my answer look like that provided on the sheet, which is x+18y37?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Oh. I figured that out. Sorry.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you all for putting forth the effort to assist me.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Or at the very least, looking over the question.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.1This is good premptive practice for me ;)
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