Let and be fixed points

MATHEMATICS · Subjective · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Let

A(2,-3)

and

B(-4,5)

be fixed points. A point

P(x,y)

moves on the straight line

2x+y=4

and forms a triangle

\triangle ABP

whose area is

6

square units. (a) Obtain the possible coordinates of

P

. (b) How many distinct positions of

P

satisfy these conditions? Give reasons for your answer.