## 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

1. FoolForMath Group Title

This is somewhat difficult, took me some time to realize the solution.

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.

Cheater. ;P

4. experimentX Group Title

y=3 ???

5. FoolForMath Group Title

No.

6. pre-algebra Group Title

Darn I need to read up on English definitions.ъ :(

7. ZhangYan Group Title

man, this is hard questions!!!

8. inkyvoyd Group Title

@FoolForMath , what do you mean by perp tangent/

9. inkyvoyd Group Title

@FoolForMath ?

10. asnaseer Group Title

is it x=0?

11. FoolForMath Group Title

Sorry, that's not the right answer.

teehee :)

13. blockcolder Group Title

When you say perpendicular tangents, do you mean two tangents lines of the curve that are perpendicular to each other?

14. cinar Group Title
15. FoolForMath Group Title

Yes, @blockcolder

16. eliassaab Group Title

If you try to do the easy problem for y = x^2, you find that the locus is the line y=-1/4.

17. blockcolder Group Title

Since the graph is symmetrical w.r.t. the y-axis, 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?

18. FoolForMath Group Title

Why do you Google Cinar? I am well aware of the answer.

19. FoolForMath Group Title

I am removing the spoiler.

20. FoolForMath Group Title

@blockcolder: looks good.

21. dumbcow Group Title

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

22. asnaseer Group Title

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.