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A point P(x,y) moves so that the sum of the distance from P to the coordinate axes is equal to the distance from P to the point A(1,1).The equation ot the locus of P in the first quadrant is ?

A point P(x,y) moves so that the sum of the distance from P to the coordinate axes is equal to the distance from P to the point A(1,1).The equation ot the locus of P in the first quadrant is ?

Grade:11

1 Answers

Arun
25763 Points
3 years ago

Distance between P and x -axis = y

Distance between P and y-axis = x

Distance between P and A(1, 1) =

\sqrt(x-1)² + (y-1)²

According to the question,

x + y = \sqrt(x-1)² + (y-1)²

On squaring both sides, we get

x² +y² + 2xy = x² +1 -2x + y² +1 -2y

2xy +2x +2y = 2

xy + x +y -1 = 0

This is the locus of point P(xy).

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