A straight line moves such that the algebraic sum of the perpendiculars drawn to it from two fixed points is equal to `2k` . Then, then straight line always touches a fixed circle of radius. (a)`2k` (b) `k/2` (c) `k` (d) none of these

Options

A. 2k
B. `k//2`
C. k
D. none of these

Answer

3

Explanation

Let two given points be A(a,0) and `B(-a,0)` and let the straight line be `y= mx +c`. Then ,
`(mx+c)/(sqrt(1+m^(2)))+(-mx+c)/(sqrt(1+m^(2)))=2k`
or `c= k sqrt(1+m^(2))`
So, the straight line is `y= mx +ksqrt(1+m^(2))`.
Clearly, it touches the circle `x^(2)+y^(2)= k^(2)` of radius k.