Tangent is drawn to the ellipse $\frac{{{x^2}}}{{27}} + {y^2} = 1$ $\left( {3\sqrt 3 \cos {\rm{\theta }},\sin {\rm{\theta }}} \right)\left[ {{\rm{where}}\,\,{\rm{\theta }} \in \left( {0,\frac{\pi }{2}} \right)} \right]$. Then, the value of $\theta $ such that sum of intercepts on axes made by this tangent is minimum, is

JEE MATHEMATICS MCQ: ELLIPSE

1 Hard

1 of 1

Application +4 | -1

Tangent is drawn to the ellipse

\frac{{{x^2}}}{{27}} + {y^2} = 1

\left( {3\sqrt 3 \cos \mathrm{\theta },\sin \mathrm{\theta }} \right)\left[ {\mathrm{where}\,\,\mathrm{\theta } \in \left( {0,\frac{\pi }{2}} \right)} \right]

. Then, the value of

\theta

such that sum of intercepts on axes made by this tangent is minimum, is

View answer and explanation

Correct option: B

\frac{\pi }{6}

Option B (

\frac{\pi }{6}

) is correct because the sum of the intercepts is minimized when

\tan \theta = \frac{1}{\sqrt 3 }

, which occurs at

\theta = \frac{\pi }{6}

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\frac{x^2}{144}+\frac{y^2}{81}=1

m

\mathrm{M}

\mathrm{mM}

P

\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1

S

S'.

A

PSS',

A

A

B

(\sqrt{7}, 0)

(-\sqrt{7}, 0)

P

9 x^{2}+16 y^{2}=144

\mathrm{PA}+\mathrm{PB}

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

r

\frac{x^2}{25}+\frac{y^2}{16}=1

P

x=0

Q

R

Q

y=x

Q

R

N P

Q

P

O