Question

Find a relation between x & y such that the point P(x,y) is equidistant from the points A(1,4) and B(1,-2).

i just want answer of this question...

Answer 1

this is the relation between x and y
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plzz correct me if there is any corrections

Answer 2

Answer:

Relation between x and y is x+y=3

Step-by-step explanation:

We are given two points A(1,4) and B(-1,2) which is equidistance from P(x,y).

Using distance formula to find the relation between x and y

PA=PB

$\sqrt{(x-1)^2+(y-4)^2}=\sqrt{(x+1)^2+(y-2)^2}$

Cancel square root both sides

$(x-1)^2+(y-4)^2=(x+1)^2+(y-2)^2$

Move x term left side and y term right side

$(x-1)^2-(x+1)^2=(y-2)^2-(y-4)^2$

$(2x)(-2)=(2y-6)(2)$

$-4x=4y-12$

$-x=y-3$

$x+y=3$

Hence, Relation between x and y is x+y=3