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Question

Equation of tangent to ellipse

$\frac{x}{{\sqrt {27} }}\cos 	heta  + \frac{y}{{\sqrt 3 }}\sin 	heta  = 1$

Area bounded by line and c

Vedclass · Accepted Answer

$9$

Vedclass · Answer

Equation of tangent to ellipse

$\frac{x}{{\sqrt {27} }}\cos 	heta  + \frac{y}{{\sqrt 3 }}\sin 	heta  = 1$

Area bounded by line and co-ordinate axis

$\Delta  = \frac{1}{2}.\frac{{\sqrt {27} }}{{\cos \,	heta }}.\frac{{\sqrt 3 }}{{\sin 	heta }} = \frac{9}{{\sin 2	heta }}$

$\Delta  = $ will be minimum when $\sin 2	heta  = 1$

${\Delta _{\min }} = 9$

If the tangent at a point on the ellipse $\frac{{{x^2}}}{{27}} + \frac{{{y^2}}}{3} = 1$ meets the coordinate axes at $A$ and $B,$ and $O$ is the origin, then the minimum area (in sq. units) of the triangle $OAB$ is

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