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The circle passing through the point (−1, 0) and touching the Y – axis at (0, 2) also passes through the point

a) $\left(\frac{-3}{2},0\right)$

b) $\left(\frac{-5}{2},0\right)$

c) $\left(\frac{-3}{2},\frac{5}{2}\right)$

d) $(-\mathrm{4,}0)$

Let a, b, c be positive real numbers such that b² – 4ac > 0 and let α₁ = c. Prove by induction that
 

Is well defined and  for n=1, 2, …

Here well defined means that the denominator in the expression of  is not zero.