For a 0, a lemniscate curve is the set of points P such that the product of the distances from P to (a, 0) and (a, 0) is a 2 Show that the equation of the lemniscate is (x 0 y 2 ) 2 2a 2 (x 2 y 2 ) Then find the equation in polar coordinates To obtain the simplest form of the equation, use the iden...

We compute the distances d 1 and d 2 of Px y from the poi ...

For a > 0, a lemniscate curve is the set of points P such that the product

Question:

For a > 0, a lemniscate curve is the set of points P such that the product of the distances from P to (a, 0) and (−a, 0) is a². Show that the equation of the lemniscate is (x 0. + y²)²= 2a²(x²− y²)

Then find the equation in polar coordinates. To obtain the simplest form of the equation, use the identity cos 2θ = cos²θ − sin²θ. Use graph plotting software and plot the lemniscate for a = 2.

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