Question

If A=(2,3) and B=(-2,1) find the equation of locus of point P such that AP^2=3PB^2​

Answer 1

correct question :

If A=(2,3) and B=(-2,1) find the equation of locus of point P such that AP²=3BP²

Step by step Explanation :

let p be the point on the locus, coordinates of p are p (x, y), and given points are A=(2,3) and B=(-2,1) ,

As we have given condition,

AP²=3BP²

(y - 3)² + (x - 2)²

=3 ( (y - 1)² + (x + 2)²)

(y² - 6y + 9 ) + (x² - 4x + 4 )

= 3( (y² - 2y + 1) + ( x² + 4x + 4))

y² + x² - 6y - 4x + 13

= 3 ( y² + x² - 2y + 4x + 5 )

y² + x² - 6y - 4x + 13

= 3y² + 3x² - 6y + 12x + 15

y² + x² - 6y - 4x + 13 -(3y² + 3x² - 6y + 12x + 15) = 0

y² + x² - 6y - 4x + 13 -3y² -3x² + 6y -12x - 15= 0

-2y² - 2x² -16x - 2 = 0

multiply by (-1) on both the sides

2y² + 2x² + 16x + 2 = 0

divide by 2 on both the sides

y² + x² + 8x + 1 = 0

x² + y² + 8x + 1 = 0 is the required equation of locus of point P.