Question
Thu December 29, 2011 By: Sunny Acharjee

Examine the position of the points(-4,3) , (1,1) and ( ?(5 )/2 ,-?3 ) w.r.t the ellipse ?4x?^2+?5y?^2=20.

Expert Reply
Thu December 29, 2011
The equation of ellipse is 4x2 + 5y2 = 20.
Here LHS = 4x2 + 5y2 and RHS = 20.
Put (-4,3), we get LHS = 4(16) + 5(9) = 64 + 45 = 109
Thus for (-4,3), LHS > RHS, so the point lies outside the ellipse.
Put (1,1), we get LHS = 4(1) + 5(1) = 9
Thus for (1,1), LHS < RHS, so the point lies inside the ellipse.
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