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

tmc2k1
10-13-2010, 10:46 PM
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!!

GMmexican
10-13-2010, 10:50 PM
Pm jibby

tmc2k1
10-13-2010, 11:31 PM
Pm jibby

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

GMmexican
10-13-2010, 11:33 PM
LOL sorry i was just kidding.......he got banned, he was the dumbest poster ever

Snake_Skinner
10-14-2010, 02:34 AM
^ How long has jibby been banned?

camar0corey
10-14-2010, 09:03 AM
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.

tmc2k1
10-14-2010, 09:53 AM
Haha wow. Never thought I would find someone in Spring Hill. Crazy indeed!

obseSSed
10-14-2010, 10:31 AM
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

-Ross-
10-14-2010, 10:40 AM
Answer, "Yes, because motorcycles don't have doors".

my bandit
10-14-2010, 11:55 AM
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)

dhowdy
10-14-2010, 12:02 PM
2x+18y*y' = 0

Z28_LT1
10-14-2010, 05:15 PM
Divide by zero, man, just divide by zero. :lol:

DiscerningZ32
10-14-2010, 05:32 PM
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...

silverM6TA
10-14-2010, 06:24 PM
ummm......google it!

tmc2k1
10-14-2010, 06:39 PM
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. :(

my bandit
10-14-2010, 08:21 PM
so (27,3) is a point on the tangent line, not the point on the ellipse that the line passes through?

malw_95z28
10-14-2010, 08:44 PM
god you guys just gave me a headache lol

Zlow28
10-14-2010, 08:51 PM
ahhh i remember when i used to be smart...

my bandit
10-14-2010, 08:53 PM
im going for engineering and my teacher said were never gonna use this shit again in our lives except for helping other with homework

Screamin_99
10-14-2010, 08:54 PM
f5 x 1838 = 1.3458 / 28 = 3 x 223

no?

LOL

Good luck man, hope you figure it out.

00ls1z
10-14-2010, 09:03 PM
It's C.. The correct answer is C..

Blakbird24
10-14-2010, 09:07 PM
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.

TrippyJoey
10-14-2010, 09:16 PM
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