<p>The curve represented by the equation \(\sqrt{px} + \sqrt{qy} = 1\), where \(p, q \in R\), \(p, q > 0\) is</p>
Step-by-Step Solution
Key Concept: Recognize that the equation √(px) + √(qy) = 1 represents a parabola by substituting u = √(px) and v = √(qy) to transform it into a linear relationship (u + v = 1), then back-substitute to get the parabolic form y = (1 - √(px))²/q.
<p><strong>Step 1:</strong> Let u = √(px) and v = √(qy), where u, v ≥ 0</p><p>Then the equation becomes: u + v = 1, or v = 1 - u</p><p><strong>Step 2:</strong> Back-substitute: √(qy) = 1 - √(px)</p><p><strong>Step 3:</strong> Square both sides: qy = (1 - √(px))²</p><p>qy = 1 - 2√(px) + px</p><p><strong>Step 4:</strong> This is of the form y = a + bx + c√(x), which is a parabola. Rearranging: √(px) = (1 - √(qy))/1 shows the relationship between √x and √y is linear, meaning x and y satisfy a quadratic relationship (parabola).</p><p><strong>Step 5:</strong> The domain is x ≥ 0, y ≥ 0, and the curve is bounded by the constraint that √(px) + √(qy) = 1, confirming a parabolic arc in the first quadrant.</p><p>∴ Answer: B</p>
Correct Answer: B