Find the area of greatest rectangle which can be inscribed in a circle of radius 10 cm.

Find a point on the curve y² = 4 x, which is nearest to the point (2, 1).

Find the point on the curve y² = 2x which is nearest to the point (1, – 4).

Find the point on the curve y² = 2x which is nearest to the point (1,  4).

Find the point on the curve x² = 8y which is nearest to the point (2, 4).

Find the point on the curve x² = 4y which is nearest to the point (–1, 2).

Find the points on the curve  which are nearest from the origin. 

Find the points on the curve  which are nearest to the point (0, 5).

A jet of an enemy is flying along the curve y = x² + 2. A soldier is placed at the point (3, 2). What is the nearest distance between the soldier and the jet?

300.

Find the maximum profit that a company can make, if the profit function is given by p (x) = 41 + 24x – 18x².