<p>Find the value of |a| for which the area of triangle included between the coordinate axes and any tangent to the curve <code>x^a y = l^a</code> is constant (where l is constant).</p>
Step-by-Step Solution
Key Concept: For curves of the form x^a y = l^a, the area of triangle formed by any tangent with coordinate axes is constant only for specific values of a.
<p><strong>Solution:</strong> For the curve $x^a y = l^a$, any tangent to this curve forms a triangle with the coordinate axes. Using the property of tangents to power-law curves, the area of the triangle formed is constant when the tangent intercepts are proportional to the curve parameters. For the curve $x^a y = l^a$, the area of the triangle formed by any tangent with the coordinate axes is constant when $|a| = 1$.</p><p>∴ |a| = 1</p>
Correct Answer: 1