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Expert: Alon Mandes - 11/3/2009


Question
)   Suppose a parabola has focus (1, 7) and directrix y = 3.  What is the equation of the parabola?

Thank you!

Answer
A parabola can be defined as the set of all points such that the distance from a point on the parabola to a focus point is the same as the distance from the directrix.
Since the focus is (1,7) and a general point on the directrix can be given by (x,3) ,
the distances from any point (x,y) on the parabola will be :
D1=(x-1)^2+(y-7)^2
D2=(x-x)^2+(y-3)^2
Now, we set D1=D2 & find the equation of the parabola :
(x-1)^2+(y-7)^2=(x-x)^2+(y-3)^2
x^2-2x+1+y^2-14y+49=y^2-6y+9
x^2-2x+41=14y
y=(1/14)x^2-(1/7)x+(41/14) . & this is the equation.  

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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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