Ellipse
Foci and Eccentricity
Grade 11
Question:
<p>Let an ellipse having major axis and minor axis parallel to x-axis and y-axis respectively. Its two foci <span>S</span> and <span>S'</span> are <span>(2, 1)</span>, <span>(4, 1)</span> and a line <span>x + y = 9</span> is a tangent to this ellipse at point <span>P</span>. Find the eccentricity of the ellipse.</p>
<p>(a) <span>1/(2√3)</span></p>
<p>(b) <span>1/√13</span></p>
<p>(c) <span>1/2</span></p>
<p>(d) <span>1/4</span></p>
Step-by-Step Solution
Key Concept: Use the property that the distance between foci is <span>2c</span>, and use the tangent condition along with the focal property to find eccentricity.
<p>Answer: (b)</p>
Correct Answer: B