With and fixed:

MATHEMATICS · Subjective · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

With

A(1,-2)

and

B(4,3)

fixed: (i) Find the equation(s) of the locus of a point

P(x,y)

for which the area of

\triangle ABP

10\,\text{square units}

. (ii) Hence show that each line obtained in part (i) is parallel to the line

AB