Given that the point (λ, λ + 1) lies inside the region bounded by the curve and y - axis.

The curve is rewritten as,

⇒ x² = 25 - y²

⇒ x² + y² = 25

⇒ S = x² + y² - 25

We know that for a point (a, b) to lie inside the circle S, the condition to be satisfied is S₁₁<0.

Applying S₁₁<0 for 1^st circle,

⇒ λ² + (λ + 1)² - 25<0

⇒ λ² + λ² + 2λ + 1 - 25<0

⇒ 2λ² + 2λ - 24<0

⇒ λ² + λ - 12<0

⇒ λ² + 4λ - 3λ - 12<0

⇒ λ(λ + 4) - 3(λ + 4)<0

⇒ (λ - 3)(λ + 4)<0

We know that the solution set of (x - a)(x - b)<0 for b>a is (a,b).

The solution set for λ is (- 4,3) ...... (1)

Since the point lies inside y - axis λ + 1>0

⇒ λ> - 1 ..... (2)

The resultant solution set is the intersection of (1) and (2).

⇒ λ((- 4,3)∩(- 1,∞))

⇒ λ(- 1,3)

∴ The correct option is (a).