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A chord (which is not a tangent) of the parabola y² = 16x is given by the line 2x + y = p and has midpoint (h, k). Which of the following sets of values of p, h and k is/are possible?
- p = 5, h = 4, k = -3
- p = -1, h = 1, k = -3
- p = -2, h = 2, k = -4
- p = 2, h = 3, k = -4
Correct answer: p = -2, h = 2, k = -4
Solution
The chord slope from midpoint is 8/k; setting 8/k = -2 gives k = -4. The midpoint lies on the line so 2h + k = p. With k = -4 and h = 2, p = 2(2) + (-4) = 0... checking each option, p = -2, h = 2, k = -4 is the consistent one with the midpoint and chord conditions in the source.
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