MCQ
If a point $(x,\;y) \equiv (\tan \theta + \sin \theta ,\;\tan \theta - \sin \theta )$, then locus of $(x, y)$ is
  • A
    ${({x^2}y)^{2/3}} + {(x{y^2})^{2/3}} = 1$
  • B
    ${x^2} - {y^2} = 4xy$
  • ${({x^2} - {y^2})^2} = 16xy$
  • D
    ${x^2} - {y^2} = 6xy$

Answer

Correct option: C.
${({x^2} - {y^2})^2} = 16xy$
c
(c) Trick : Put the value of $(x, y)$ $ \equiv $ ($\tan \theta + \sin \theta ,\,\tan \theta - \sin \theta )$ in option $(c)$, which satisfies the equation.

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