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">\(\ne\)</span> 1 then (a + b) is equal to:</p>
<p style="display:inline">8</p>
<p style="display:inline">-1</p>
<p style="display:inline">3</p>
<p style="display:inline">7</p>
Step-by-Step Solution
Key Concept: If a family of chords passes through a fixed point $P$ on a circle, the perpendicular to the chord at its other endpoint $B$ always passes through the point diametrically opposite to $P$.
<p>7</p>
Correct Answer: D