<p>A line cuts the x-axis at A(α, 0) and the y-axis at B(0, β). A point P(4, 3) divides AB in the ratio 2:1. The equation of the line is:</p>
Step-by-Step Solution
Key Concept: Use the section formula to express P's coordinates in terms of α and β, then solve the system of equations: if P divides AB in ratio 2:1, then P = ((2·0 + 1·α)/(2+1), (2·β + 1·0)/(2+1)).
<p><strong>Step 1:</strong> Use section formula. If P(4, 3) divides AB in ratio 2:1 (where A is (α, 0) and B is (0, β)):</p><p>P = ((2·0 + 1·α)/(2+1), (2·β + 1·0)/(2+1)) = (α/3, 2β/3)</p><p><strong>Step 2:</strong> Equate coordinates:</p><p>α/3 = 4 ⟹ α = 12</p><p>2β/3 = 3 ⟹ β = 9/2</p><p><strong>Step 3:</strong> The line passes through A(12, 0) and B(0, 9/2). Using intercept form:</p><p>x/12 + y/(9/2) = 1</p><p>x/12 + 2y/9 = 1</p><p>Multiply by 36: <strong>3x + 8y = 36</strong></p><p>∴ Answer: A</p>
Correct Answer: A