Question
Question: If (λ - 2) x<sup>2</sup> + λy<sup>2</sup> = 4 represents a rectangular hyperbola then λ equals:...
If (λ - 2) x2 + λy2 = 4 represents a rectangular hyperbola then λ equals:
A
0
B
2
C
1
D
3
Answer
1
Explanation
Solution
Condition for rectangular hyperbola
∆ ≠ 0, (λ - 2) λ ≠ 0 ⇒ λ ≠ 2, λ ≠ 0
h2 > ab ⇒ λ (λ - 2) < 0 0 < λ < 2
coefficient of x2 + coefficient of y2 0.
⇒ λ - 2 + λ = 0
λ = 1.