Coordinate Geometry

The locus of the foot of perpendicular drawn from the center of the ellipse x2 + 3y2 = 6 on any tangent to it is

  1. (x2 - y2)2 = 6x2 + 2y2
  2. (x2 - y2)2 = 6x2 - 2y2
  3. (x2 + y2)2 = 6x2 - 2y2
  4. (x2 + y2)2 = 6x2 + 2y2

Answer

Let the foot of perpendicular be P(h,k)

Equation of tangent with slope m passing P(h, k) is

y = mx ± √(6m2 + 2), where m = -h/k

√(6h2/k2 + 2) = (h2 + k2)/k

6h2 + 2k2 = (h2 + k2)2

The correct option is D.