Problem #171
Given a curve in the first quadrant, consider the triangle formed
by the tangent line to the curve at a given point and the two
coordinate axes.

Find a curve such that the area of the triangle is independent of
the point on the curve.

Find a curve such that the length of the hypotenuse of the triangle
is independent of the point on the curve.

Find a curve such that the sum of the length of the two legs of
the triangle is independent of the point on the curve.

Find a curve such that the sum of the lengths of a leg and the
hypotenuse of the triangle is independent of the point on the curve.

Find a curve such that the perimeter of the triangle is independent of
the point on the curve.
The solution will be posted shortly.
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