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The line y = mx + c (m > 0) is a focal chord of the parabola y² = -64x and is also tangent to the circle (x + 10)² + y² = 4. Find the value of 4*sqrt(2)*(m + c).

1. 34
2. 40
3. 44
4. 52

Correct answer: 34

Solution

Using the focus condition c = 16m and the tangency to the circle of radius 2 gives m and c whose combination yields 4*sqrt(2)*(m + c) = 34.

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