Question

The bifolium, pictured below, has the equation


`(x^(2) + y^(2))^(2)= 4xy^(2)`
Find the x-coordinate of the two marked points at which the tangent line is horizontal. (The two marked points do not lie on the y-axis.)

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Answer 1

The x coordinate of the two marked points at which the tangent line is horizontal is x = 0.75

How to find the x coordinate

The x coordinate is solved by drawing a straight line from each.

The point is traced to where the line intersects the x-axis.

The point is noted and this is the required point.

In this case, the points are in same straight line as shown in attached figure. The line intersects the x-axis halfway between 0.7 and 0.8.

This point is 0.75