Binomial Theorem

Question
CBSEENMA11015517

An ellipse is drawn by taking a diameter of the circle (x–1)2 + y2 = 1 as its semiminor 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

  • 4x2+ y2 = 4

  • x2 +4y2 =8

  • 4x2 +y2 =8

  • x2+4y2 =16

Solution

D.

x2+4y2 =16

The equation of the ellipse.
Diameter of circle (x-1)2 +y2 = 1 is 2 and that of circle x2 +(y-2)2 = 4 is 4 units.
⇒ Semi-minor axis of ellipse, b =2 units are semi major axis of ellipse, a  4 unite
Hence, the equation of the ellipse is 
straight x squared over straight a squared plus straight y squared over straight b squared space equals space 1
rightwards double arrow space straight x squared over 16 plus straight y squared over 4 space equals 1
rightwards double arrow space straight x squared space plus 4 straight y squared space equals space 16

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