Question

The locus of a point which moves difference of its distance from two fixed straight which are at right angles is equal to the distance from another fixed straight line is
A. a stright line
B. a circle
C. a parabola
D. an ellipse

Answer 1

Correct Answer - A
Take the two fixed straight lines as OX and OY. Let `x cos alpha + y sin alpha` be another fixed straight line . Let (h,k) be the variable point. Then, as per given condition
`k- h = h cos alpha + k sin alpha -p`
`rArr h (1+ cos alpha) + k (sin alpha + 1) -p = 0`
So locus of (h,k) is
`x (1+cos alpha) + y (sin alpha -1) -p = 0`, which is a straigh line.