If the point (k + 1, k) lies inside the region bound by the curve $x = \sqrt{25-y^2}$ and the y-axis, then the integral value of k

Problem: If the point (k + 1, k) lies inside the region bound by the curve $x = \sqrt{25-y^2}$ and the y-axis, then the integral value of k is / are

(A) 0

(B) 1

(C) 2

(D) 3

Solution: Circle

Since (k + 1, k) lies inside the region bounded by $x = \sqrt{25-y^2}$

⇒ (k + 1)2 + k2 – 25 < 0 and k + 1 > 0

⇒ 2k2 + 2k – 24 < 0 and k > –1

⇒ –4 < k < 3 and k > –1

⇒ –1 < k < 3

Hence (A), (B) and (C) are the correct answer.