A line moves such that the portion of it intercepted between the coordinate axes is of constant length (a ), then the locus of the mid point of that line segment is

Step-by-step solution

Let (A=(p, 0) ) (B=(0, q) ) Let ( P=(h, k) ) be the mid-point of ( A B ). ( array rlrl Given, A B & =a (h, k) & = mid-point of A B (h, k) & = ( p 2 , q 2 ) & p & =2 h, q=2 k & A & =(p, 0)=(2 h, 0) & B & =(0, q)=(0,2 k) array ) Since, length of (A B=a ) ( aligned (2 h)^2+(2 k)^2 & =a 4 h^2+4 k^2 & =a 4 h^2+4 k^2 & =a^2 h^2+k^2 & = a^2 4 aligned ) ( ) Required locus is (x^2+y^2= a^2 4 ) ( ) Hence, solution is (c).