Ellipse
Eccentricity of Ellipse
Grade 11
Question:
<p>Let an ellipse having major axis and minor axis parallel to x-axis and y-axis respectively. Its two foci S and S′ are <span>(2, 1)</span> and <span>(4, 1)</span> and a line <span>x + y = 9</span> is a tangent to this ellipse at point P. Find the eccentricity of the ellipse.</p>
<p>(a) <span>\frac{1}{2\sqrt{3}}</span></p>
<p>(b) <span>\frac{1}{\sqrt{13}}</span></p>
<p>(c) <span>\frac{1}{2}</span></p>
<p>(d) <span>\frac{1}{4}</span></p>
Step-by-Step Solution
Key Concept: Use the properties of ellipse with given foci and tangent condition to find eccentricity. Distance between foci gives 2ae, and the tangent condition provides additional constraint.
<p>Solution not provided in source material.</p>
Correct Answer: B