COMEDK · Maths · 27. Application of Derivatives
The maximum area in square units of an isosceles triangle inscribed in an ellipses \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) with its vertex at one end of the major axis is
- A \(\sqrt{3} a b\) sq units
- B \(\frac{3 \sqrt{3}}{4} a b\) sq units
- C \(\frac{5 \sqrt{3}}{4} a b\) sq units
- D None of these
Answer & Solution
Correct Answer
(B) \(\frac{3 \sqrt{3}}{4} a b\) sq units
Step-by-step Solution
Detailed explanation
Let \(\triangle A B C\) be an isosceles triangle inscribed in the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\). Let coordinate of \(A\) be \((a, 0)\). Area of \(\triangle A B C, A=\frac{1}{2} \times A D \times B C\)…
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