<p>The equation of chord AB is y(l + 3) = 4(x + l). Show that this represents a family of lines passing through a fixed point, and find that point.</p>
Step-by-Step Solution
Key Concept: A family of lines equation can be decomposed into two linear equations whose intersection is the fixed point.
<p><strong>Step 1:</strong> Rewrite the equation as:</p><p>$$(3y - 4x) + l(y - 4) = 0$$</p><p><strong>Step 2:</strong> This is of the form L₁ + λL₂ = 0 representing a family of lines.</p><p><strong>Step 3:</strong> The fixed point is found by solving:</p><p>3y - 4x = 0 and y - 4 = 0</p><p>This gives y = 4 and x = 3, so the fixed point is (3, 4).</p><p>∴ Answer is (c).</p>
Correct Answer: C