Question

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

Answer 1

Given curve is x2 + 2y2 = 6

Since the tangent is parallel to the line, so dy/dx = –1

⇒ – x/2y = –1

⇒ x = 2y when x = 2y, then 4y2 + 2y2 = 6

⇒ 6y2 = 6

⇒ y2 = 1

⇒ y = ±u20091 when y = ±u20091, then x = ±u20092

So, the point on the curve is (2, 1) or (– 2, –1).