Racer's Lounge - Need some help on a calculus problem

Find the equations of both the tangent lines to the ellipse x^2 + 9y^2 = 81 that pass through the point (27, 3).

I need to find the horizontal line and the non-horizontal line.

I figured out the horizontal line is y=3, but how do I find the non-horizontal line?

I would like it if someone told me how to do this step by step and not just the answer.

Thanks!!

Pm jibby

Pm jibby

Whats his full username? Says jibby doesn't exist.

LOL sorry i was just kidding.......he got banned, he was the dumbest poster ever

^ How long has jibby been banned?

You're in Spring Hill? Sorry I can't help you with your math problem, I have never seen your car! That's just crazy. Looks like it would stick right out.

Haha wow. Never thought I would find someone in Spring Hill. Crazy indeed!

you're correct; y = 3.

Plug y into the equation of the ellipse where y = the equation you used to solve for it. Which was y = m(X-27)+3... right? Or am I way off?

I haven't had calculus in over 10 years... don't judge me

Answer, "Yes, because motorcycles don't have doors".

2x + 18y' = 0 (implicit differentiation)
18y' = -2x (isolating y')
y' = -x/9 (solving for y')
f'(27) = -27/9 = -3 (slope of tangent line)
3 = -3(27) + b (substituting point and slope to find b)
84 = b (solving for b)
y = -3x + 84 (equation of the line)

2x+18y*y' = 0

Divide by zero, man, just divide by zero. :lol:

I'm so glad I don't have to take calculus anymore.
I think it was actually more interesting than Finance though.

Oh, uh... I can't help with your problem.
Whah whah...

ummm......google it!

2x + 18y' = 0 (implicit differentiation)
18y' = -2x (isolating y')
y' = -x/9 (solving for y')
f'(27) = -27/9 = -3 (slope of tangent line)
3 = -3(27) + b (substituting point and slope to find b)
84 = b (solving for b)
y = -3x + 84 (equation of the line)

Thanks for attempting, but thats not the correct answer for the problem. You are assuming the point (27,3) is a point on the ellipse, but unfortunately its not. I know the correct answer is:

y= 1/4x - 15/4. I just have no clue how to get to that though. :(

so (27,3) is a point on the tangent line, not the point on the ellipse that the line passes through?

god you guys just gave me a headache lol

ahhh i remember when i used to be smart...

im going for engineering and my teacher said were never gonna use this shit again in our lives except for helping other with homework

f5 x 1838 = 1.3458 / 28 = 3 x 223

no?

LOL

Good luck man, hope you figure it out.

It's C.. The correct answer is C..

im going for engineering and my teacher said were never gonna use this shit again in our lives except for helping other with homework

He's right. Algebra, Geometry and Trig you will use CONSTANTLY. But Calculus, not so much. I have yet to come across an application where Calculus really helped me. Realistically, we now use software to do all this stuff. It does help to understand where the numbers that you put on the prints came from though.

It's C.. The correct answer is C..

The correct answer is never C!

BTW I think the non horizontal line is:
x^2+9y^2=81
x^2=81-9y^2
x=(81-9y^2)^(1/2)
then you just get the derivative dx/dy