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Let L be the tangent line to the parabola y² = 4x - 20 at the point (6, 2). If L is also tangent to the ellipse x²/2 + y²/b = 1, find the value of b.

1. 14
2. 11
3. 16
4. 20

Correct answer: 14

Solution

The tangent to y² = 4x-20 at (6,2) is x - y - 4 = 0 (slope 1). For the ellipse x²/2 + y²/b = 1 with line y = x - 4, the tangency condition gives c² = a² m² + b: 16 = 2(1) + b, so b = 14.

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