jee-main 2018 Q70

jee-main · India · 15apr Tangents, normals and gradients Normal or perpendicular line problems

If $\beta$ is one of the angles between the normals to the ellipse $x ^ { 2 } + 3 y ^ { 2 } = 9$ at the points $( 3 \cos \theta , \sqrt { 3 } \sin \theta )$ and $( - 3 \sin \theta , \sqrt { 3 } \cos \theta ) ; \theta \in \left( 0 , \frac { \pi } { 2 } \right) ;$ then $\frac { 2 \cot \beta } { \sin 2 \theta }$ is equal to :
(1) $\frac { 1 } { \sqrt { 3 } }$
(2) $\frac { \sqrt { 3 } } { 4 }$
(3) $\frac { 2 } { \sqrt { 3 } }$
(4) $\sqrt { 2 }$

If $\beta$ is one of the angles between the normals to the ellipse $x ^ { 2 } + 3 y ^ { 2 } = 9$ at the points $( 3 \cos \theta , \sqrt { 3 } \sin \theta )$ and $( - 3 \sin \theta , \sqrt { 3 } \cos \theta ) ; \theta \in \left( 0 , \frac { \pi } { 2 } \right) ;$ then $\frac { 2 \cot \beta } { \sin 2 \theta }$ is equal to :\\
(1) $\frac { 1 } { \sqrt { 3 } }$\\
(2) $\frac { \sqrt { 3 } } { 4 }$\\
(3) $\frac { 2 } { \sqrt { 3 } }$\\
(4) $\sqrt { 2 }$

Paper Questions

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