If the equation kxy + 10x + 8y + 16 = 0 represents a pair of lines, then

MHT CET 2025 Mathematics question

If the equation represents a pair of lines, then

(A)k = 5 onlyCorrect
(B)k = 0 only
(C)k = 0 or k = 5
(D)the value of k does not exist

Answer: (A)

Solution

Compare with ax^2+2hxy+by^2+2gx+2fy+c=0: , , , , , . A pair of lines needs abc+2fgh-af^2-bg^2-ch^2=0, i.e. or . But for the equation becomes , which is a single

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Question ID VK-101218