Question

Let P be a point lying on given family of lines satisfying the condition $|PA| \le 4$ where $\lambda$ ∈ [-2,-1], then the area of the region sketched by locus of P is kπ, then the value of k is - 16

• A. 16
• B. -16
• C. 8
• D. -8

Answer 1

Answer: (A)

16

Answer 2

The condition $|PA| \le 4$ implies that point P lies within or on a circle of radius $R=4$ centered at A. The family of lines, parameterized by $\lambda \in [-2, -1]$, likely defines a sector of this circle. The problem statement is contradictory as it states the area is $k\pi$ and then asserts $k=-16$. Geometric area cannot be negative. Assuming a typo and that the locus of P covers the entire disk (which would happen if the family of lines sweeps an angle of $2\pi$ radians), the area would be $\pi R^2 = \pi (4^2) = 16\pi$. Comparing this to $k\pi$, we get $k=16$. This is the most plausible intended answer in a standard mathematical context, despite the contradictory information provided.