If a point $(x,y) = (\tan {\rm{\theta }} + \sin {\rm{\theta }},\tan {\rm{\theta }} - \sin {\rm{\theta }}),$ then locus of $\left( {x,y} \right)$ is

${\left( {{x^2}y} \right)^{2/3}} + {\left( {x{y^2}} \right)^{2/3}} = 1$

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

1 of 1

Analyzing +4 | -1

If a point

(x,y) = (\tan \mathrm{\theta } + \sin \mathrm{\theta },\tan \mathrm{\theta } - \sin \mathrm{\theta }),

then locus of

\left( {x,y} \right)

View answer and explanation

Correct option: C

{\left( {{x^2} - {y^2}} \right)^2} = 16xy

Option C (

{\left( {{x^2} - {y^2}} \right)^2} = 16xy

) is correct because it is the locus of the point (x, y) when x = tan θ + sin θ and y = tan θ - sin θ.