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

- 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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- chestercat

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- IsTim

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

So, first, dy/dx=-x/dy.
I then subbed in (1,2) and got -1/18.

- anonymous

Lol uhh so I cant give answers so ill just leave now but what youv done so far is correct :D

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## More answers

- IsTim

I don't need the answer. I need to know what my process afterwards should be.

- inkyvoyd

What's the derivative?

- inkyvoyd

And Chad is in 11th grade, he won't be able to help you

- IsTim

1. Derivative is 2x+18y(dy/dx)=0. Right?
2. I figured that out already...

- anonymous

lol ink I can give him an answer ;D

- inkyvoyd

x^2+9y^2=37
dy/dx 37=dy/dx x^2+dy/dx 9y^2
0=2x+18y dy/dx

- inkyvoyd

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

I already have the answer in my textbook and potentially Wolfram Alpha. I need to know how to GET there though.

- inkyvoyd

Normally at this point I try to isolate dy/dx for convenience

- anonymous

from conic section?

- inkyvoyd

0=2x+18y dy/dx
(-2x)/(18y)=dy/dx
x/(-9y)=dy/dx

- IsTim

Yeah, I think I did that.It's -x/dy right?
@ Shruti: I don't think so...

- inkyvoyd

And, my answer agrees with your answer here.

- inkyvoyd

Although my work here is moot, because i'm in 9th grade.

- IsTim

Ok. Thanks for the help so far.

- IsTim

Ok. How would I get to the answer of x+18y-37=0 from knowing that the slope is -1/18?

- inkyvoyd

eh?

- inkyvoyd

If you had the derivative and wanted to get the original equation?

- IsTim

I guess?

- IsTim

@shruti By conics did you mean http://www.purplemath.com/modules/circle3.htm

- amistre64

since this is an equation of an ellipse, y can be considered an implicit function of x right?

- IsTim

I guess. My notes only reveal the steps. This work is not from a textbook.

- IsTim

In fact, it's not even addressed in my textbook. That's strange.

- amistre64

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

If you have the derivative, and want to get the original equation, you take the anti-derivative of it

- inkyvoyd

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

Otherwise, I might have to look into it.

- IsTim

Y' is -x/dy, which, when we sub in (1,2) is -1/18 right?

- anonymous

yes tim, -1/18 is right

- IsTim

What would I do next then?

- inkyvoyd

Well, you have a point, and a slope.

- inkyvoyd

(1,2) -> point
-1/18 -> slope

- inkyvoyd

remember, y=mx+b

- IsTim

Would I sub those into y=mx+b?

- anonymous

you have slope, you have a point, put it in point slope form...

- inkyvoyd

put in the point and the slope, and then you have b

- inkyvoyd

then, put in y=mx+b, cept don't put in that point

- inkyvoyd

This isn't a calculus problem, this is an algebra problem, :D

- IsTim

Sorry, what is point slope form?
It's algebra? I must really have been "dumbing" down these years...

- inkyvoyd

Ok.

- inkyvoyd

There's multiple ways of writing the equation for a line.

- inkyvoyd

This is point slope: y-y1=m(x-x1)

- inkyvoyd

this is slope intecept: y=mx+b

- inkyvoyd

This is standard form: ax+by=c

- inkyvoyd

I normally work with slope intercept, because i'm more used to it.

- inkyvoyd

However, point slope is the fastest way to go here.

- inkyvoyd

y-y1=m(x-x1)
(x1,y1)=(1,2)
m=-1/18

- IsTim

The answer is in the form of ax+by=c I guess, but I am also more familiar with slope intercept.

- IsTim

Wait, I already have the slope...
I know it is -1/18.
But how do I get to x+18y-37?

- inkyvoyd

y-1=(-1/18)(x-2)
now, just isolate y, and distribute x

- inkyvoyd

They have given you the point that the line must pass through, and you have found the slope,

- IsTim

Oh. I finally understand. Thank you very much. I will call out again if I need help.

- inkyvoyd

Ok. :D

- IsTim

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

Yes

- inkyvoyd

I got it confused myself. xD

- IsTim

Why doesn't my answer look like that provided on the sheet, which is x+18y-37?

- IsTim

Oh. I figured that out. Sorry.

- IsTim

Thank you all for putting forth the effort to assist me.

- IsTim

Or at the very least, looking over the question.

- inkyvoyd

No problem :)

- inkyvoyd

This is good premptive practice for me ;)

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