The pairs of straight lines ax^2+2hxy-ay^2=0 and hx^2-2axy-hy^2=0 are such that

JEE Advanced Mathematics question

The pairs of straight lines and are such that

(A)one pair bisects the angles between the other pairCorrect
(B)the lines of one pair are equally inclined to the lines of the other pairCorrect
(C)the lines of one pair are perpendicular to the lines of the other pair
(D)none of these

Answer: (A),(B)

Solution

The bisectors of are , i.e. , which is exactly the second pair. Likewise the bisectors of the second pair are , i.e. , which is the first pair. - (a) True, as just shown. - (b) True:

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Question ID VK-108881