The tangent to x2-y2-a2 having inclinations - and - intersect at P- If -0- then the locus of P is-

The correct option is C xy=0 Given that cotα+cotβ=0 ⇒ tanβ= tanα ⇒β=180 α Since α+β=180 , The two tangents should intersect on either ...

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Standard XII

Mathematics

Slope Form a Line

The tangent t...

Question

The tangent to $x^{2} + y^{2} = a^{2}$ having inclinations $α$ and $β$ intersect at $P$ . If $cot α + cot β = 0$ , then the locus of $P$ is:

x + y = 0

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x - y = 0

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x y = 0

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x y = 1

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Solution

The correct option is C $x y = 0$
Given that $c o t α + c o t β = 0$
$\Rightarrow t a n β = - t a n α$
$\Rightarrow β = 180 - α$
Since $α + β = 180$ , The two tangents should intersect on either $x$ axis or $y$ axis
Therefore atleast one of $x$ , $y$ should be $0$
Therefore the locus of $P$ is $x y = 0$
Therefore the correct option is $C$

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The tangent to x2+y2=a2 having inclinations α and β intersect at P. If cotα+cotβ=0, then the locus of P is:

The correct option is C xy=0Given that cotα+cotβ=0⇒tanβ=−tanα⇒β=180−αSince α+β=180 , The two tangents should intersect on either x axis or y axisTherefore atleast one of x , y should be 0Therefore the locus of P is xy=0Therefore the correct option is C

The tangent to $x^{2} + y^{2} = a^{2}$ having inclinations $α$ and $β$ intersect at $P$ . If $cot α + cot β = 0$ , then the locus of $P$ is: