alleryCommon tangent to circle x² + y² = 5 and parabola y² = 8x:
Ay = 0
BTwo of form y = ±x + c via tangency conditions
CCannot determine
Dy = x + 2
Answer & Solution
Correct answer: B. Two of form y = ±x + c via tangency conditions
**Tangent to circle (radius sqrt(5)):** y = mx ± sqrt(5)sqrt(1+m²).
Tangent to parabola y² = 8x (a=2): y = mx + 2/m.
For common tangent, set 2/m = ±sqrt(5)sqrt(1+m²).
**Squaring:** 4/m² = 5(1+m²)
→ 5m⁴ + 5m² - 4 = 0. Solutions for m² give specific common tangents.
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