Math miscellaneousHard

Question

The lines p(p2 + 1) x - y + q = 0 and (p2 + 1)2 x + (p2 + 1)y + 2q = 0 are perpendicular to a common line for

Options

A.no value of p
B.exactly one value of p
C.exactly two values of p
D.more than two values of p

Solution

Lines must be parallel, therefore slopes are equal ⇒ p(p2 + 1) = - (p2 + 1) ⇒ = - 1

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