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An ellipse with major and minor axis length as 2a and 2b units touches coordinate axis in first quadrant. If foci are (x1,y1) and (x2,y2), then the value of x1x2+y1y2 is
  1. 2b2
  2. a2b2
  3. a2+b2
  4. 2a2


Solution

The correct option is A 2b2
We know that product of length of perpendicular from foci upon any tangents to ellipse is b2.

Hence from the diagram, x1 and x2 are the length of perpendiculars from foci upon tangent y axis of the given ellipse, thus x1x2=b2
Similarly y1y2=b2
x1x2+y1y2=2b2

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