Question:
<p>Let x + 2y - 5 + <span class="math-tex">\(\lambda\)</span> (x + 3y - 7) = 0 be a variable chord of the circle x<sup>2</sup> + y<sup>2</sup> - 4x - 6y + 11 = 0. If perpendiculars are drawn at the end points of these chords pass through a fixed point (a, b), a <span class="math-tex">\(\neq \)</span> 1 then (a + b) is equal to :</p>
<p style="display:inline">-1</p>
<p style="display:inline">3</p>
<p style="display:inline">7</p>
<p style="display:inline">8</p>
Step-by-Step Solution
Key Concept: Since the fixed point $P(1, 2)$ lies on the circle, every variable chord is of the form $PA$, and the line perpendicular to the chord at the variable endpoint $A$ always passes through the point $(a, b)$ diametrically opposite to $P$.
<p>7</p>
Correct Answer: C