Given that the circle x2 + y2 + 2ax + 8y + 16 = 0 touches x - axis. We need to find the value of a.
We know that the value of y on the x - axis is 0.
⇒ x2 + (0)2 + 2ax + 8(0) + 16 = 0
⇒ x2 + 2ax + 16 = 0
The quadratic equation will have similar roots if the circle touches the x - axis.
We know that for the quadratic equation ax2 + bx + c = 0 the condition to be satisfied for the equal roots is b2 - 4ac = 0
⇒ (2a)2 - 4(1)(16) = 0
⇒ 4a2 - 64 = 0
⇒ a2 = 16
⇒ a = ±4
∴The correct option is (b).
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