For two distinct fixed points and

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

For two distinct fixed points

A(a_1,b_1)

and

B(a_2,b_2)

, a point

P(x,y)

moves so that the area of

\triangle APB

is a non–zero constant

k

square units. (i) Obtain the equation representing the locus of

P

. (ii) Prove that the locus consists of two straight lines parallel to the line

AB

. (iii) Express the distance between these two lines in terms of

k

and the length

AB

. (iv) What change occurs in the locus when

k=0

? Justify your answer.