Highly selective Backlog Qs for JEE MainMathematicsHyperbola
The equation x 2 + y - 1 2 - x 2 + y + 1 2 =   K will represent a hyperbola for -
Options
- AK ∈ 0 , 2
- BK ∈ 0 , 1
- CK ∈ 1 , ∞
- DK ∈ 0 , ∞
Correct answer
A. K ∈ 0 , 2
Step-by-step solution
We have x 2 + y - 1 2 - x 2 + y + 1 2 = K Which is equivalent to S 1 P - S 2 P = C o n s t . Where S 1 ≡ 0 , 1 , S 2 ≡ 0 , -1 .and P ≡ x , y Using properties of a hyperbola, the above equation represents a hyperbola, then we have. 2 a = K [where 2 a is the transverse axis and e is the eccentricity] and 2 a e = S 1 S 2 = 2 Dividing, we have e = 2 K Since, e > 1 for a hyperbola, therefore K < 2 Also, K must be a positive quantity. Hence, we have, K ∈ 0 , 2 .