a point p (x y) moves so that the sum of the distances from p to the coordinates axes is - Maths - Straight Lines

Question

a point p (x y) moves so that the sum of the distances from p to
the coordinates axes is equal to the distance from p to the point
A91,1) the equation of the locus of p in the first quadrant will be
?

ramandeep.singh · Accepted Answer

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

$x^{2} + y^{2} + 2 x y = x^{2} - 2 x + 1 + y^{2} - 2 y + 1 \Rightarrow 2 x y = - 2 x - 2 y + 2 ∴ x + y + x y - 1 = 0$

This is the locus of point P(x, y).

a point p (x y) moves so that the sum of the distances from p to the coordinates axes is equal to the distance from p to the point A91,1). the equation of the locus of p in the first quadrant will be ?