Question:
<p>If <span class="math-tex">\(\left(a, \frac{1}{a}\right)\)</span> and <span class="math-tex">\(\left(b, \frac{1}{b}\right)\)</span> be the extremities of chord on hyperbola <span class="math-tex">\(x y=1\)</span>, then line perpendicular to this chord will be equally inclined to co-ordinate axes if</p>
<p style="display:inline"><span class="math-tex">\(a^2 b^2=1\)</span></p>
<p style="display:inline">none of these</p>
<p style="display:inline"><span class="math-tex">\((a+b)^2=1\)</span></p>
<p style="display:inline"><span class="math-tex">\(a^2=b^2\)</span></p>
Step-by-Step Solution
Key Concept: A line equally inclined to the coordinate axes has a slope of ±1, which corresponds to the negative reciprocal of the chord's slope -1/ab.
<p><span class="math-tex">$a^2 b^2=1$</span></p>
Correct Answer: A