If the tangent at a point on the ellipse x²/27 + y²/3 = 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:<p></p>

y = mx ± √(a²m² + b²)
y = mx ± √(27m² + 3)
Intercept on X axis = √(27m² + 3)/m
Intercept on Y axis = √(27m² + 3)
Area = 1/2 × √(27m² + 3)/m × √(27m² + 3) = 1/2 × (27m² + 3)/m
AM ≥ GM
27m² + 3/m ≥ √(27m × 3/m) ≥ 9
Minimum Value = 9

Eduprobe

Question:

If the tangent at a point on the ellipse x²/27 + y²/3 = 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:

Solution: