Let a and b be the lengths of the semimajor and semiminor axes of an ellipse respectively. Draw a rectangle whose two sides are tangent to the ellipse and the other two are normal to the ellipse. Find the area enclosed by the locus of the vertex of the rectangle at which the normals meet. The figure shows a triangle divided into six regions using line segments drawn from the vertices to the opposite sides. The red and blue regions have the same areas of 1 unit. What should be the area of the yellow region so that the area of the whole triangle is minimum? Let function f(x) = alnx + vx + 1 for> > 0, where a is a real number and a * 0. If VIE -2, +00 ). f(x) 0