<p>A conic passes through the point (2, 4) and is such that the segment of any of its tangents at any point contained between the co-ordinate axes is bisected at the point of tangency. Then the foci of the conic are:</p>
<p style="display:inline">(<span class="math-tex">\(2 \sqrt{2}\)</span>, 0) and (<span class="math-tex">\(-2 \sqrt{2}\)</span>, 0)</p>
<p style="display:inline">(4, 4) and (-4, -4)</p>
<p style="display:inline">(<span class="math-tex">\(2 \sqrt{2}\)</span>, <span class="math-tex">\(2 \sqrt{2}\)</span>) and (<span class="math-tex">\(-2 \sqrt{2}\)</span>, <span class="math-tex">\(-2 \sqrt{2}\)</span>)</p>
<p style="display:inline">(<span class="math-tex">\(4 \sqrt{2}\)</span>, <span class="math-tex">\(4 \sqrt{2}\)</span>) and (<span class="math-tex">\(-4 \sqrt{2}\)</span>, <span class="math-tex">\(-4 \sqrt{2}\)</span>)</p>
Step-by-Step Solution
Key Concept: The property that the tangent segment between the coordinate axes is bisected at the point of tangency uniquely defines a rectangular hyperbola with the axes as its asymptotes, following the differential equation dy/dx = -y/x.
<p>(4, 4) and (-4, -4)</p>
Correct Answer: B