EllipseHard
Question
The ellipse E1 : 
= 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E2 is
= 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E2 isOptions
A.
B.
C.
D.
Solution
Equation of ellipse is (y + 2) (y - 2) + λ (x + 3) (x - 3) = 0
It passes through (0, 4) ⇒ λ =
Equation of ellipse is
Alternate
Let the ellipse be
as it is passing through (0, 4) and (3, 2). So, b2 = 16 and
⇒ a2 = 12
So, 12 = 16 (1 - e2)
⇒ e = 1/2.
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