If the ellipse x24+y21=1 meet the ellipse x21+y2a2=1 in four distinct points and

Question

If the ellipse

\frac{x^{2}}{4} + \frac{y^{2}}{1} = 1

meet the ellipse

\frac{x^{2}}{1} + \frac{y^{2}}{a^{2}} = 1

in four distinct points and

a = b^{2} - 10 b + 25

, then the value b does not satisfy

Options:

A . (−∞,4)

B . (4, 6)

C . (6,−∞)

D . [4, 6]

Answer: Option D
:
D
For the two ellipse to intersect at four different points

1 < a^{2} \Rightarrow 1 < (b - 5)^{2} \Rightarrow b / ϵ [4, 6]

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