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$Length of the perpendicular from the centre of the ellipse 27 x^{2} + 9 y^{2} = 243 on a tangent drawn to it which makes$
$equal intercepts on the coordinates axes is$

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Correct option is C

Ellipse x29+y227=1 Tangent to ellipse having slope m is y=mx±a2m2+b2 Since tangent makes equal intercepts on the coordinate axes, m=-1∴ Equation of tangents are y=−x±6 or x+y±6=0 Length of perpendicular from (0,0)=62=32

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Length of the perpendicular from the centre of the ellipse27x2+9y2=243 on a tangent drawn to it which makes equal intercepts on the coordinates axes is

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$Length of the perpendicular from the centre of the ellipse 27 x^{2} + 9 y^{2} = 243 on a tangent drawn to it which makes$
$equal intercepts on the coordinates axes is$