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.
Back to the Advanced Problem Archives
Back to the Math Department Homepage.