Coordinate Geometry

An ellipse is drawn by taking a diameter of the circle (x - 1) + y = 1 as its semi-minor axis and a diameter of the circle x2 + (y - 2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

  1. x2 + 4y2 = 8
  2. 4x2 + y2 = 4
  3. x2 + 4y2 = 16
  4. 4x2 + y2 = 8

Answer

Semi minor axis b = 2

Semi major axis a = 4

Equation of ellipse = x2/a2 + y2/b2 = 1

The correct option is D.