Question:
Area lying in the first quadrant and bounded by ellipse \(4x^2 + 9y^2 = 144\) is _____
Area lying in the first quadrant and bounded by ellipse \(4x^2 + 9y^2 = 144\) is _____
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Area in first quadrant of symmetric curves like ellipse = one-fourth of total area.
Updated On: Apr 2, 2026
- \( 24\pi \)
- \( 8\pi \)
- \( 12\pi \)
- \( 6\pi \)
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The Correct Option is D
Solution and Explanation
Concept:
Standard equation of ellipse:
\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]
Area of full ellipse = \( \pi ab \)
Step 1: Convert to standard form. \[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \] So, \( a = 6, \; b = 4 \)
Step 2: Find total area. \[ \text{Area} = \pi ab = \pi \cdot 6 \cdot 4 = 24\pi \]
Step 3: First quadrant area. \[ \frac{1}{4} \times 24\pi = 6\pi \]
Step 1: Convert to standard form. \[ \frac{x^2}{36} + \frac{y^2}{16} = 1 \] So, \( a = 6, \; b = 4 \)
Step 2: Find total area. \[ \text{Area} = \pi ab = \pi \cdot 6 \cdot 4 = 24\pi \]
Step 3: First quadrant area. \[ \frac{1}{4} \times 24\pi = 6\pi \]
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