The curve with the equation 2(x² + y2)? = 25(x² – y) is called a lemniscate (shown below). (a) Find an equation of the tangent line to the curve at (3,1). (b) At how many points does the curve have horizontal tangents? (c) Estimate the coordinates of these points [Hint: Read off the coordinates from the x – and y – axes. Use fractions.] yA 4 2 1 -4 3 -2 -1 1 2 3 4 -1 -2 -3 -4 3,

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