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The tangent to the parabola y² = 24x at (alpha, beta) is perpendicular to the line 2x + 2y = 5. For the hyperbola x²/alpha² - y²/beta² = 1, the normal at the point (alpha + 4, beta + 4) does NOT pass through which point?
- (25, 10)
- (20, 12)
- (30, 8)
- (15, 13)
Correct answer: (15, 13)
Solution
Tangent slope 1 gives the contact point, fixing alpha and beta; constructing the hyperbola normal at (alpha+4, beta+4) and testing the points shows (15,13) is not on it.
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