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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

- IsTim

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

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## 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 ;)

Looking for something else?

Not the answer you are looking for? Search for more explanations.