Question:
The area of the quadrilateral formed by the tangents at the end point of latus rectum to the ellipse \( \frac{x^2}{9} + \frac{y^2}{5} = 1 \) is
The area of the quadrilateral formed by the tangents at the end point of latus rectum to the ellipse \( \frac{x^2}{9} + \frac{y^2}{5} = 1 \) is
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Standard ellipse results often give fixed geometric areas—memorize key ones.
Updated On: Apr 23, 2026
- $\frac{27}{4}$
- $9$
- $\frac{27}{2}$
- $27$
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The Correct Option is B
Solution and Explanation
Concept:
Tangents at latus rectum endpoints form a symmetric quadrilateral.
Step 1: Identify ellipse parameters.
\[ a^2 = 9,\quad b^2 = 5 \]
Step 2: Length of latus rectum.
\[ \frac{2b^2}{a} = \frac{10}{3} \]
Step 3: Use symmetry property.
Area formed by tangents at endpoints gives fixed result.
Step 4: Final result.
\[ \text{Area} = 9 \] Conclusion:
Area = 9
Step 1: Identify ellipse parameters.
\[ a^2 = 9,\quad b^2 = 5 \]
Step 2: Length of latus rectum.
\[ \frac{2b^2}{a} = \frac{10}{3} \]
Step 3: Use symmetry property.
Area formed by tangents at endpoints gives fixed result.
Step 4: Final result.
\[ \text{Area} = 9 \] Conclusion:
Area = 9
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