MathDB

Problem 1

Part of 1996 VJIMC

Problems(2)

tangent to ellipse, triangle has minimal area

Source: VJIMC 1996 1.1

10/12/2021
On the ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 find the point T=(x0,y0)T=(x_0,y_0) such that the triangle bounded by the axes of the ellipse and the tangent at that point has the least area.
geometryconicsellipseintegrationcalculus
finite number of parabolas cover plane

Source: VJIMC 1996 2.1

10/13/2021
Is it possible to cover the plane with the interiors of a finite number of parabolas?
conicsparabolageometry