AP EAMCET202422 May 2024Evening ShiftMathematicsHyperbolaActual
If the equation x^2 7-k + y^2 5-k =1 represents a hyperbola then
Options
- A5 k 7
- Bk 5 or k 7
- Ck 5
- Dk 5, k 7,- k
Correct answer
A. 5 k 7
Step-by-step solution
A x^2+ B x y+ C y^2+ D x+ E y+ F =0 represents a hyperbola if B^2-4 A C 0, A C Given equation : x^2 7-k + y^2 5-k =1 A = 1 5-k , ~B =0, C = 1 7-k So, -4 ( 1 5-k ) ( 1 7-k ) 04 ( 1 k-5 ) ( 1 k-7 ) 0 5 k 7