If the point `(lambda,lambda+1)` lies inside the region bounded by the curve `x=sqrt(25-y^2)` and y-axis , then `lambda` belongs to the interval
(a) `(-1,3)` (b) `(-4,3)` (c) `(-oo,-4)uu(3,oo)` (d) none of these

Explanation

` x=\sqrt{25-y^{2}} `

`implies x^2 = 25 - y^{2}`

`implies x^2 + y^{2} = 25 `

It is given that the point `(lambda, lambda + 1)` lies in the region which is bounded by the curve` x=\sqrt{25-y^{2}} `and y - axis.
As the point (a, b) to lie inside the circle C, the condition to be satisfied is `C_{11} < 0`.

Applying `C_{11}< 0` for first circle,

`\Rightarrow \lambda ^{2}+(\lambda +1)^{2}-25< 0`

`\Rightarrow \lambda ^{2}+\lambda ^{2}+2\lambda +1-25< 0`

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