The lines pp2+1x−y+q=0 and p2+12x+p2+1y+2q=0 are pendicular to a line L for

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The lines $p (p^{2} + 1) x - y + q = 0 and {(p^{2} + 1)}^{2} x + (p^{2} + 1) y + 2 q = 0$ are pendicular to a line L for

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exactly one value of p

exactly two values of p

more than two values of p

no value of p

answer is A.

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Detailed Solution

We know that, lines perpendicular to the same line are parallel to each other. Therefore slope of both the lines will be same.

i.e. $p (p^{2} + 1) = - (p^{2} + 1) \Rightarrow p = - 1$

$∴$ There is exactly one value of $p$ .

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