The number of integral values of p in the domain [-5,5], such that the equation 2x^2+4xy-py^2+4x+qy+1=0 represents pair of lines, are

MHT CET 2023 Mathematics question

The number of integral values of p in the domain [-5,5], such that the equation represents pair of lines, are

(A)3
(B)4
(C)7
(D)8Correct

Answer: (D)

Solution

Compare with ax^2+2hxy+by^2+2gx+2fy+c=0: . A pair of lines needs \Delta=abc+2fgh-af^2-bg^2-ch^2=0. Substituting, . Setting gives , which has a real q only if the

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Question ID VK-095359