Question

4. Find the relation between x and y if point P(x,y) is
equidistant from the points A (5,1) and B(-1,5).
Note: Write the steps where formula is applied and the final
relation.​

Answer 1

Question

Find the relation between X and y if point P ( x,y ) is equidistant from the points A ( 5, 1 ) and B ( -1 , 5 ).

Given

• A ( 5 , 1 ) and B ( -1 , 5 )

Required to Find

Relation between X and Y

Solution

Let the point P ( x , y ) is equidistant from the points A ( 3 , 6 ) and B ( -3 , 4 )

so, PA = PB

By using distance formula

$\sf \implies \sqrt{( x_{2} - x_{1} {)}^{2} + ( y_{2} - y_{1} {)}^{2} }$

Here we go...!

$\sf\implies \: \sqrt{(x - 3 {)}^{2} + (y - 6 {)}^{2} } = \sqrt{(x + 3 {)}^{2} + (y - 4 {)}^{2} }$

$\sf\implies \: (x - 3 {)}^{2} + (y - 6 {)}^{2} = (x + 3 {)}^{2} + (y - 4 {)}^{2}$

$\sf\implies \: {x}^{2} - 6x + 9 + {y}^{2} - 12y + 36 = {x}^{2} + 6x + 9 + {y}^{2} - 8y + 16$

$\sf \implies - 6x - 6x - 12 + 8y + 36 - 16 = 0$

$\sf\implies - 12x - 4y + 20 = 0$

$\sf \implies3x + y - 5 = 0$

Hence this is the relation between X and y