Q.

A(5, 3) and B(3, –2) are two fixed points. Find the equation of locus of P, so that the area of triangle PAB is 9 sq. units.

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Detailed Solution

Given points are A = (5, 3), B = (3, –2)
Let P(x, y) is any point on the locus
Given condition is area of PAB  9sq.units
area of
PAB=12x1y2y3+x2y3y1+x3y1y212|5(2y)+3(y3)+x(3+2)|=9|105y+3y9+5x|=18|5x2y19|=185x2y19=±185x2y19=18 or 5x2y19=185x2y37=0 or 5x2y1=0
locus of P(x, y) is (5x – 2y – 37) (5x–2y–1) = 0

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