Question

If the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{1}$ meet the ellipse $\frac{x^{2}}{1} + \frac{y^{2}}{a^{2}} = 1$ in four distinct points and a = b² – 10b + 25, then the value b does not satisfy

• A. (-∞, 4]
• B. (4, 6)
• C. [6, ∞)
• D. [4, 6]

Answer 1

Answer: (D)

$4, 6$

Answer 2

Now according to condition a>1

b² – 10b + 25 = a>1

⇒ b² – 10b + 24 > 0

⇒ (b – 4)(b- 6) > 0 ie., b<4 and b>6

⇒ b ∉ [4, 6]