Ellipse
Circumscribed Parallelograms
Grade 11
Question:
<p>A parallelogram circumscribes the ellipse \(\frac{x^2}{9} + \frac{y^2}{4} = 1\) and two of its opposite angular points lie on straight lines \(x^2 = l^2\), \(l \neq 0\). The locus of the other two vertices is:</p>
<p>(a) ellipse if \(l > 3\)</p>
<p>(b) hyperbola if \(l \in (0, 3)\)</p>
<p>(c) circle if \(l = \frac{9}{5}\)</p>
<p>(d) ellipse if \(l \in (0, 3)\)</p>
Step-by-Step Solution
Key Concept: The locus type depends on the value of the parameter \(l\) relative to the semi-major axis of the ellipse.
<p>Use properties of circumscribed parallelograms and the given ellipse equation to determine the locus based on the parameter \(l\).</p>
Correct Answer: a, b, c