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Expert: Alon Mandes - 12/1/2008


Question
Find the point(s) on the hyperbola x²-y²=4 that is closest to the point (1,3)

Answer
Hello John,
This question was sent to the question's pool. But I see that no
one had solved it, so I decided to do that.

Distance form (xo,yo) to (1,3) is :
D=√√ [ (xo-1)^2 + (yo-3)^2 ].
We know that xo^2-yo^2=3 & that gives us xo=√[4-yo^2]. Therefore :
D=√ [ (√[4-yo^2] - 1)^2 + (yo-3)^2 ].
D'=0 ->  2(√[4-yo^2] - 1)^2 * 2yo/2√[4-yo^2] + 2(yo-3)=0 ->

( 1-√[4-yo^2] )
--------------   = 3-yo   ->
√[4-yo^2]


1-√[4-yo^2]=√[4-yo^2]*(3-yo) ->
1=√[4-yo^2]*[1+3-yo] ->
1=√[4-yo^2]*[4-yo] ->
1=[4-yo^2][4-yo]^2
Solving this 4th degree polynom gives us : y0=1.94 -> xo=0.48  .

Alon.  

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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