Advanced Math practice question

Answer: 4

Substitute: x² + (x + k)² = 8 → 2x² + 2kx + k² − 8 = 0. Tangency means one solution, so the discriminant is 0: 4k² − 8(k² − 8) = 0 → k² = 16 → k = 4.

Common wrong answers

If you answered 8

8 is the constant in the circle's equation, not k.

If you answered 16

16 is k², before taking the square root.

If you answered 2.83

2.83 is √8, the radius, which is not the y-intercept of the tangent line.

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