The points and are fixed

MATHEMATICS · Single correct · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

The points

A(1,2)

and

B(4,-1)

are fixed. The locus of a point

P(x,y)

for which

\text{area}(\triangle APB)=5\text{ square units}

is a pair of straight lines. Which of the following pairs represents this locus? (a)

x+y=\dfrac{14}{3}\text{ or }x+y=\dfrac{4}{3}

(b)

x+y=\dfrac{19}{3}\text{ or }x+y=-\dfrac{1}{3}

(c)

x-y=\dfrac{19}{3}\text{ or }x-y=-\dfrac{1}{3}

(d)

x+y=\dfrac{10}{3}\text{ or }x+y=-\dfrac{10}{3}