Any harder question? (1 Viewer)

[Richard Lee]

Hi, everyone
If u got any hard question. u can post here. I am sure that I can help u and send whole solution to your email.
Trust me!

 

[Rahul]

P(ct, c/t) lies on teh rectangular hyperbola xy = c^2. the normal at P meets the hyperbola again at Q. M is the midpioint of PQ. Find teh equation of the locus of M.

 

[underthesun]

Send to mail or post here? I reckon you should post here instead of sending to mail..

 

[turtle_2468]

a/sqrt(a^2+8bc) + b/sqrt(b^2+8ca) + c/sqrt(c^2+8ab) >= 1

 

[Fosweb]

haha...

 

[ND]

Originally posted by Rahul
P(ct, c/t) lies on teh rectangular hyperbola xy = c^2. the normal at P meets the hyperbola again at Q. M is the midpioint of PQ. Find teh equation of the locus of M.

Equation of normal of xy=c^2 at P(ct, c/t):
y - c/t = t^2*(x-ct)
solving with xy=c^2:
t^3*x^2 + (c-ct^4)x - c^2*t = 0
now the x-value of M is the sum of roots of this eqn:
M_x = (ct^4-c)/t^3

similarly:
M_y = (c-ct^4)/t

M[(ct^4-c)/t^3, (c-ct^4)/t]

-y/x = t^2

subbing into the y-value of m gives:

y = (c-c*y^2/x^2)/sqrt(-y/x)
x^4*c^2 - 2*c^2*x^2*y^2 + y^4*c^2 + x^3*y^3

There may be a silly error in there somwhere.

edit: Hmmm i'm not sure whether you needed help with this q, or whether you were just giving it to him. Oh well...

 

[ND]

Originally posted by turtle_2468
a/sqrt(a^2+8bc) + b/sqrt(b^2+8ca) + c/sqrt(c^2+8ab) >= 1

lol.

 

[Rahul]

Originally posted by ND
Hmmm i'm not sure whether you needed help with this q, or whether you were just giving it to him. Oh well...

yes the latter is correct
sorry

 

[ND]

Originally posted by Rahul
yes the latter is correct
sorry

Well i don't think i had done a conics q since the trials, so it was good for me anyway.

 

[Rahul]

haha
good to hear. i just picked out the last question from arnold's further questions to test him out.

 

[Affinity]

1)
x+y=1
x,y E R+
m,n E N
prove (1-y^m)^n + (1-x^n)^m >= 1

2)
given m colours to paint the vertices of an octohedron, find the number of possible different octohedrons, a colour can be used up to 6 times.

 

[Richard Lee]

Originally posted by turtle_2468
a/sqrt(a^2+8bc) + b/sqrt(b^2+8ca) + c/sqrt(c^2+8ab) >= 1

Hi there:
Find the answer to the thread " I want more inequality question"

 

[Richard Lee]

Originally posted by Rahul
P(ct, c/t) lies on teh rectangular hyperbola xy = c^2. the normal at P meets the hyperbola again at Q. M is the midpioint of PQ. Find teh equation of the locus of M.

If the solution is:
c*(x^2-y^2)^2=-4*x^3*y^3
Contact me. I will send u the fully solution.
If not, it's appreciated to imform me.

 

[Archman]

Originally posted by Richard Lee
Hi there:
Find the answer to the thread " I want more inequality question"

there is an error in your proof, refer to " I want more inequality question"

 

[Richard Lee]

Originally posted by Archman
there is an error in your proof, refer to " I want more inequality question"

Sorry about that! Go to "I want inequality question"