The minimum area of the triangle formed by any tangent to the ellipse x 2 a 2 + y 2 b 2 = 1 and the coordinate axes is
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Equation of tangent to given ellipse is
y=mx+a2m2+b2−−−−−−−−√
It meets axes at (−a2m2+b2−−−−−−−√m,0) and (0,a2m2+b2−−−−−−−−√)
∴ Area of triangle
=12∣∣a2m2+b2m∣∣
=12∣∣∣a2m+b2m∣∣≥ab
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