Question

A(-5,2)and B(4,1) Find the equation of the locus of point P, which is equidistant from A and B​

Answer 1

Hello ❤️

X+y=6

Let us consider a point p equidistant from point A and B with coordinates X and Y .

According to distance formula

The distance between any two arbitrary point C (x1 ,y1) and D (y2,y2)

✓(x1 - x2)² + ( y1 -y2)²

Since point P is equidistant from point A and B

Hence PA = PB

✓ (x-5)²+(y-2)²=

✓(x-4)²+(y-1)²

x²-10×x+25+y²-4×y+4=x²-8×x+16+y²-2×y+1

2×x +2×y= 29-17

X+y=6

Hence equation the locus of point p is given by

X+ Y= 6