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 $a=b^2-10b+25$, then the value b does not satisfy

• A. $(-\infty ,4)$
• B. (4, 6)
• C. $(6,-\infty )$
• D. [4, 6]

Answer 1

The correct option is D [4, 6]

For the two ellipse to intersect at four different points
$1<a^2\Rightarrow 1<(b-5{)}^2\Rightarrow b\text{/}ϵ[4,6]$