The locus of a point which moves such that difference of its distance from two fixed straight which are at right angles is equal to the distance from another fixed straight line is

Options

A. a straight line
B. a circle
C. a parabola
D. an ellipse

Answer

A

Explanation

Let the two fixed straight lines be the coordinate axes and let the third line be x - y =0
Let P(h,k) be a variable point . Then ,
`| |h| - |k|| = |(h-k)/(sqrt2)"|" " " ` [Given]
`implies |h| - |k| = pm (h-k)/(sqrt2)`
`therefore` Locus of P (h,k) is `|x| - |y| = pm ((x - y)/(sqrt2))`
Clearly , it represents a straight line .
Hence , option (a) is correct .