Question:
Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is \(\frac{3}{5}\) and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :
Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is \(\frac{3}{5}\) and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :
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Find a = 5 and b = 4; the rhombus formed by the four vertices has area 2ab.
Updated On: Nov 11, 2026
- 8
- 32
- 80
- 40
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The Correct Option is D
Solution and Explanation
Distance between foci \(= 2ae = 6\), so \(ae = 3\). With \(e = \frac35\), \(a = 5\).
\(b^2 = a^2(1-e^2) = 25 \cdot \frac{16}{25} = 16\), so \(b = 4\).
The vertices are \((\pm5, 0)\) and \((0, \pm4)\); they form a rhombus with diagonals 10 and 8.
Area \(= \frac12 \cdot 10 \cdot 8 = 40\) sq. units.
Answer: (4) 40
\(b^2 = a^2(1-e^2) = 25 \cdot \frac{16}{25} = 16\), so \(b = 4\).
The vertices are \((\pm5, 0)\) and \((0, \pm4)\); they form a rhombus with diagonals 10 and 8.
Area \(= \frac12 \cdot 10 \cdot 8 = 40\) sq. units.
Answer: (4) 40
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