Question

P(x, y) is a point on the perpendicular bisector of the segment AB joining A(2,3) and B(-4,1).Find the relation between x and y.

Answer 1

Given points are A(2,3) and B(-4,1).

Here,

= > (x1,y1) = (2,3)

= > (x2,y2) = (-4,1)

Midpoint of AB = (x1 + x2/2, y1 + y2/2)

= > (2 - 4/2, 3 + 1/2)

= > (-1,2).

Now,

Slope of AB = (y2 - y1)/(x2 - x1)

= > (1 - 3)/(-4 - 2)

= > -2/-6

= > 1/3.

Therefore,

Slope of the required line = -1/1/3

= > -3.

The equation of the required line is:

= > y - y1 = m(x - x1)

= > y - 2 = -3(x + 1)

= > y - 2 = -3x - 3

= > -3x - y - 1 = 0

= > 3x + y + 1 = 0.

Therefore, the relation between x and y = 3x + y + 1 = 0

Hope this helps!

Answer 2

2²+x²-4x + 3² + y² -6y = 4²+x²+8x+1²+y²-2y

4+x² -4x +9+y² -6y = 16 + x² + 8x + 1 + y²- 2y

x²+y²-4x-6y+13-16-1-x²-y²-8x+2y = 0

-12x - 4y - 4 = 0

-4 ( 3x + y + 1 ) = 0

Therefore ,

3x + y + 1 = 0

Required relation is 3x + y + 1 = 0

I hope this helps you.

: )