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Let a, r, s, t be nonzero real numbers and let P(at², 2at), Q(ar², 2ar), S(as², 2as) be distinct points on the parabola y² = 4ax. Suppose PQ is a focal chord and the line QR is parallel to PK, where K is the point (2a, 0). Find the value of r.
- -1/t
- (t² + 1)/t
- 1/t
- (t² - 1)/t
Correct answer: (t² + 1)/t
Solution
Since PQ is a focal chord, the parameter at Q is -1/t. The condition QR parallel to PK (K = (2a,0)) leads, after using the slope relation, to r = (t² + 1)/t.
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