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The locus of point of intersection of lines  \mathrm{x \cos \alpha+y \sin \alpha=a\, and \, x \sin \alpha-y \cos \alpha=b} is  ( \mathrm{\alpha} is variable)

Option: 1

\mathrm{2\left(x^{2}+y^{2}\right)=a^{2}+b^{2}}


Option: 2

\mathrm{x^{2}-y^{2}=a^{2}-b^{2}}


Option: 3

\mathrm{x^{2}+y^{2}=a^{2}+b^{2}}


Option: 4

None of these


Answers (1)

best_answer

Let the point of intersection be (\mathrm{h}, \mathrm{k})

Hence \mathrm{h \cos \alpha+k \sin \alpha=a}
Hence the locus is
\mathrm{x^{2}+y^{2}=a^{2}+b^{2}}

Hence (C) is the correct answer.

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