Question

PLEASE HELP
Use implicit differentiation to find an equation of the tangent line to the ellipse x^2/2 + y^2/72 = 1 at (1,6)

Answer 1

is someone actually going to reply...?

Answer 2

\[
\frac d{dx}\frac{x^2}2+\frac d{dx}\frac{y^2}{72}=\frac d{dx}1\\
\frac{x^3}6+\frac d{dy}\frac{y^2}{72}\times\frac{dy}{dx}=0\\
\frac{y^3}{216}\times\frac{dy}{dx}=-\frac{x^3}6\\
\frac{dy}{dx}=-\frac{x^3}6\times\frac{216}{y^3}=-\frac{36x^2}{y^2}=-\frac{36x^2}{y^2}
\]

Answer 3

@lamp12345 sorry I saw @G-unit was replying so I didn't reply

Answer 4

@kc_kennylau thats not an answer choice:

-12x+8
-5x+10
-10x+8
-8x+10
-6x+12

Answer 5

Well it's not finished

Answer 6

you have to substitute x=1 and y=6 to find the slope of the tangent

Answer 7

oh ok

Answer 8

1. Substitute x=1 and y=6 to the derivative to find out the slope
2. Substitute x=1 and y=6 to the original function to find out the point cut by the tangent.
3. Point-slope form
4. Convert it to slope-intercept form by making y the subject

Answer 9

ok i did that and didn't get an exact answer but it was closest to -6x+12.

Answer 10

Okay, first we want to take the derivative of both sides.

d/dx (x^2)/2 + (y^2)/72 = d/dx 1
d/dx (x^2)/2 + (y^2)/72 = 0

So the derivative of x^2/2 is x. If you need that explained as well let me know but it's pretty basic.

x + d/dx (y^2)/72 = 0

Here's where it might get a little confusing.
Let's go ahead and isolate the d/dx (y^2)/72 so it doesn't get messy.

When you take the d/dx of a y variable, here's the rule.
You basically treat it like an x, and multiple it by dy/dx

So it becomes dy/dx(2y) * 1/72
Or simplified to (1/36y) dy/dx

Now we plug it back in to what we already had:

x + (1/36y) dy/dx = 0
Move the x to the other side
(1/36y) dy/dx = -x
Divide by 1/36y

dy/dx = -36x/y


Substitute in the x=1 and y=6
-36(1)/6

=-6 is the slope of the tangent line

Now do the tangent work, and you should get the correct answer. I think Kenny's answer was off which is why you didn't get the correct result.

Answer 11

@G-unit so my answer was correct? -6x+12

Answer 12

oh wait you said I didnt get the correct result. whats the tangent work I have to do @G-unit

Answer 13

y - 6 = -6 (x-1)
y - 6 = -6x + 6
y = -6x + 12

Yes, it is the answer.

Answer 14

thanks!