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For the parabola y² = 16x, a chord that is not a tangent has the equation 2x + y = p, and its midpoint is (h, k). Which of the following values for p, h, and k are valid?
- p = 5, h = 4, k = -3
- p = 2, h = 3, k = -4
- p = -2, h = 2, k = -4
- p = -1, h = 1, k = -3
Correct answer: p = 2, h = 3, k = -4
Solution
The equation of the chord and the midpoint of the chord must satisfy the equation of the parabola, resulting in a system of equations that can be solved to find the valid values of p, h, and k, which are p = 2, h = 3, and k = -4.
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