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Expert: - 5/3/2006


Question
I'm studing maths. Could you provide me with help on this question:
x^2=4(x^2-y^2)
1) Find the four points where the tangent is horizontal
2) Find the two points where the tangent is vertical
Thank you very much
Hope to hear from you soon
Emma

Answer
Hi, Emma,

You wrote:
Subject:  The Eight Curve (or lemniscate) differentiation
Question:  I'm studing maths. Could you provide me with help on this question:

x^2 = 4(x^2-y^2)
1) Find the four points where the tangent is horizontal
2) Find the two points where the tangent is vertical
Thank you very much
Hope to hear from you soon
Emma
-------------------------------
Something is wrong here.  Your equation is not at all a lemniscate.  It simplifies:

x^2 = 4x^2 - 4y^2

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

which is a pair of straight lines crossing at the origin.

Please correct and resend.

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