IsTim
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
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I've gotten the slope of -1/18, but I don't know if that's correct. And if so, how do I continue?
IsTim
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So, first, dy/dx=-x/dy.
I then subbed in (1,2) and got -1/18.
CHAD159753
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Lol uhh so I cant give answers so ill just leave now but what youv done so far is correct :D
IsTim
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I don't need the answer. I need to know what my process afterwards should be.
inkyvoyd
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What's the derivative?
inkyvoyd
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And Chad is in 11th grade, he won't be able to help you
IsTim
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1. Derivative is 2x+18y(dy/dx)=0. Right?
2. I figured that out already...
CHAD159753
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lol ink I can give him an answer ;D
inkyvoyd
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x^2+9y^2=37
dy/dx 37=dy/dx x^2+dy/dx 9y^2
0=2x+18y dy/dx
inkyvoyd
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No, 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
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I already have the answer in my textbook and potentially Wolfram Alpha. I need to know how to GET there though.
inkyvoyd
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Normally at this point I try to isolate dy/dx for convenience
shruti
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from conic section?
inkyvoyd
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0=2x+18y dy/dx
(-2x)/(18y)=dy/dx
x/(-9y)=dy/dx
IsTim
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Yeah, I think I did that.It's -x/dy right?
@ Shruti: I don't think so...
inkyvoyd
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And, my answer agrees with your answer here.
inkyvoyd
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Although my work here is moot, because i'm in 9th grade.
IsTim
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Ok. Thanks for the help so far.
IsTim
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Ok. How would I get to the answer of x+18y-37=0 from knowing that the slope is -1/18?
inkyvoyd
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eh?
inkyvoyd
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If you had the derivative and wanted to get the original equation?
IsTim
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I guess?
amistre64
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since this is an equation of an ellipse, y can be considered an implicit function of x right?
IsTim
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I guess. My notes only reveal the steps. This work is not from a textbook.
IsTim
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In fact, it's not even addressed in my textbook. That's strange.
amistre64
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it 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
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If you have the derivative, and want to get the original equation, you take the anti-derivative of it
inkyvoyd
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If you're asking about taking anti-derivatives (indefinite integrals), and have not yet learned about rieman sums, don't worry about the question
inkyvoyd
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Otherwise, I might have to look into it.
IsTim
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Y' is -x/dy, which, when we sub in (1,2) is -1/18 right?
dpaInc
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yes tim, -1/18 is right
IsTim
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What would I do next then?
inkyvoyd
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Well, you have a point, and a slope.
inkyvoyd
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(1,2) -> point
-1/18 -> slope
inkyvoyd
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remember, y=mx+b
IsTim
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Would I sub those into y=mx+b?
dpaInc
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you have slope, you have a point, put it in point slope form...
inkyvoyd
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put in the point and the slope, and then you have b
inkyvoyd
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then, put in y=mx+b, cept don't put in that point
inkyvoyd
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This isn't a calculus problem, this is an algebra problem, :D
IsTim
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Sorry, what is point slope form?
It's algebra? I must really have been "dumbing" down these years...
inkyvoyd
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Ok.
inkyvoyd
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There's multiple ways of writing the equation for a line.
inkyvoyd
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This is point slope: y-y1=m(x-x1)
inkyvoyd
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this is slope intecept: y=mx+b
inkyvoyd
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This is standard form: ax+by=c
inkyvoyd
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I normally work with slope intercept, because i'm more used to it.
inkyvoyd
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However, point slope is the fastest way to go here.
inkyvoyd
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y-y1=m(x-x1)
(x1,y1)=(1,2)
m=-1/18
IsTim
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The answer is in the form of ax+by=c I guess, but I am also more familiar with slope intercept.
IsTim
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Wait, I already have the slope...
I know it is -1/18.
But how do I get to x+18y-37?
inkyvoyd
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y-1=(-1/18)(x-2)
now, just isolate y, and distribute x
inkyvoyd
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They have given you the point that the line must pass through, and you have found the slope,
IsTim
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Oh. I finally understand. Thank you very much. I will call out again if I need help.
inkyvoyd
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Ok. :D
IsTim
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Wait, 1 and 2 in y-1=(-1/18)(x-2)/ Shouldn't it be y-2=(-1/18)(x-1)? Because (1,2)?
inkyvoyd
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Yes
inkyvoyd
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I got it confused myself. xD
IsTim
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Why doesn't my answer look like that provided on the sheet, which is x+18y-37?
IsTim
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Oh. I figured that out. Sorry.
IsTim
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Thank you all for putting forth the effort to assist me.
IsTim
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Or at the very least, looking over the question.
inkyvoyd
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No problem :)
inkyvoyd
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This is good premptive practice for me ;)