Question

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

Answer 1

I've gotten the slope of -1/18, but I don't know if that's correct. And if so, how do I continue?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

What's the derivative?

Answer 6

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

Answer 7

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

Answer 8

lol ink I can give him an answer ;D

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

from conic section?

Answer 14

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

Answer 15

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

Answer 16

And, my answer agrees with your answer here.

Answer 17

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

Answer 18

Ok. Thanks for the help so far.

Answer 19

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

Answer 20

eh?

Answer 21

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

Answer 22

I guess?

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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'

Answer 28

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

Answer 29

If you're asking about taking anti-derivatives (indefinite integrals), and have not yet learned about rieman sums, don't worry about the question

Answer 30

Otherwise, I might have to look into it.

Answer 31

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

Answer 32

yes tim, -1/18 is right

Answer 33

What would I do next then?

Answer 34

Well, you have a point, and a slope.

Answer 35

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

Answer 36

remember, y=mx+b

Answer 37

Would I sub those into y=mx+b?

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

Ok.

Answer 44

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

Answer 45

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

Answer 46

this is slope intecept: y=mx+b

Answer 47

This is standard form: ax+by=c

Answer 48

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

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

Ok. :D

Answer 57

Wait, 1 and 2 in y-1=(-1/18)(x-2)/ Shouldn't it be y-2=(-1/18)(x-1)? Because (1,2)?

Answer 58

Yes

Answer 59

I got it confused myself. xD

Answer 60

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

Answer 61

Oh. I figured that out. Sorry.

Answer 62

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

Answer 63

Or at the very least, looking over the question.

Answer 64

No problem :)

Answer 65

This is good premptive practice for me ;)