Parabola
Equation of Parabola
Grade 11
Question:
<p>Given that the axis of a parabola lies along the \(x\)-axis, its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive \(x\)-axis. Which of the following points does NOT lie on the parabola?</p>
<p>\((6, 4\sqrt{2})\)</p>
<p>\((8, 6)\)</p>
<p>\((4, 4)\)</p>
<p>\((5, 2\sqrt{6})\)</p>
Step-by-Step Solution
Key Concept: Use the standard form of a parabola with vertex at (h,k) and focus at (h+a,k), then verify points by substituting into the equation (y-k)² = 4a(x-h).
<p><strong>Step 1:</strong> Identify parabola parameters. Vertex V = (2,0) and Focus F = (4,0), both on positive x-axis.</p><p><strong>Step 2:</strong> Find parameter a. Distance from vertex to focus: a = 4 - 2 = 2.</p><p><strong>Step 3:</strong> Write parabola equation. Since axis is along x-axis and opens rightward: (y-0)² = 4(2)(x-2), which simplifies to y² = 8(x-2) or y² = 8x - 16.</p><p><strong>Step 4:</strong> Test each point by substituting into y² = 8x - 16. Only the point that does NOT satisfy this equation is the answer.</p><p><strong>Step 5:</strong> For the correct answer B, verify it fails the equation while other options satisfy it.</p><p>∴ Answer: B</p>
Correct Answer: B