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FoolForMath
Group Title
Fool's problem of the day,
\(1.\)Find the locus of the intersection of the perpendicular tangents drawn to the curve \(4y^3=27x^2 \).
Good luck!
 2 years ago
 2 years ago
FoolForMath Group Title
Fool's problem of the day, \(1.\)Find the locus of the intersection of the perpendicular tangents drawn to the curve \(4y^3=27x^2 \). Good luck!
 2 years ago
 2 years ago

This Question is Closed

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
This is somewhat difficult, took me some time to realize the solution.
 2 years ago

rebeccaskell94 Group TitleBest ResponseYou've already chosen the best response.0
Where does one start to find the answer to this question ? you can msg me so you don't give it away if you want, I just wanna know HOW to solve it.
 2 years ago

rebeccaskell94 Group TitleBest ResponseYou've already chosen the best response.0
Cheater. ;P
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
y=3 ???
 2 years ago

prealgebra Group TitleBest ResponseYou've already chosen the best response.0
Darn I need to read up on English definitions.ъ :(
 2 years ago

ZhangYan Group TitleBest ResponseYou've already chosen the best response.0
man, this is hard questions!!!
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
@FoolForMath , what do you mean by perp tangent/
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
@FoolForMath ?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
is it x=0?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Sorry, that's not the right answer.
 2 years ago

ladiesman123 Group TitleBest ResponseYou've already chosen the best response.0
teehee :)
 2 years ago

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
When you say perpendicular tangents, do you mean two tangents lines of the curve that are perpendicular to each other?
 2 years ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=plot+4y^3%3D27x^2
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Yes, @blockcolder
 2 years ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.0
If you try to do the easy problem for y = x^2, you find that the locus is the line y=1/4.
 2 years ago

blockcolder Group TitleBest ResponseYou've already chosen the best response.0
Since the graph is symmetrical w.r.t. the yaxis, I'll consider first x>0. By implicit differentiation, we have: \[4y^3=27x^2\\ 12y^2y'=54x\\ y'=\frac{54x}{12y^2}=\frac{9x}{2y^2}\] Am I on the right track?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
Why do you Google Cinar? I am well aware of the answer.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
I am removing the spoiler.
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.1
@blockcolder: looks good.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
the set of points that represent the intercepts of the perpendicular tangents match the original function. all the intercepts lie on the same curve it was a little bit of work so i won't post my solution here...the steps were 1) find dy/dx, then the perpendicular slope is dx/dy 2) solve for line equations for each slope 3) set them equal to find intercept points
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
ok  I misunderstood the question. I took it to mean the intersection of the lines that are perpendicular to the tangents to the given curve.
 2 years ago
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