The fixed points and are the ends of one side of a variable triangle

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

Problem

The fixed points

A(-2,3)

and

B(6,7)

are the ends of one side of a variable triangle

\triangle ABP

. The point

P(x,y)

moves so that the area of the triangle is always

15

square units. (i) Derive the equation of the locus of

P

. (ii) Show that the locus consists of two parallel straight lines. (iii) Determine the perpendicular distance between these two lines.