Parabola
Chords of Parabola
Grade 11

Question:

<p>Let \(y = g(x)\) intersect \(y = f(x)\) at two distinct points A, B. The slope of \(g(x)\) if the length of segment AB is 4 units is:</p>
<p>(a) ±1</p>
<p>(b) ±2</p>
<p>(c) ±3</p>
<p>(d) ±4</p>

Step-by-Step Solution

Key Concept: Set up the intersection equation g(x) = f(x), use the chord length formula \(|AB| = \sqrt{1+m^2}\cdot|x_2-x_1|\), and solve for the slope m.
<p>Let \(y = g(x) = mx + c\) be the line passing through P. Setting \(g(x) = f(x)\) gives a quadratic equation.</p><p>For the chord with endpoints A and B, the distance formula combined with the discriminant gives: \(|AB| = 4\).</p><p>Solving yields \(m = ±2\).</p>
Correct Answer: b

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