Question

Find a point on the curve x² + 2y² = 6 whose distance from the line x + y = 7, is minimum.

Answer 1

Let us take a point P (√6 cos θ, √3 sin θ) on x²/6 + y²/3 = 1 Now, to minimise the distance from P to given straight line x + y= 7, shortest distance exists along the common normal.