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Find a Relation Between X and Y Such that the Point (X, Y) is Equidistant from the Points (3, 6) and (−3, 4). - CBSE Class 10 - Mathematics

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Question

Find a relation between x and y such that the point (xy) is equidistant from the points (3, 6) and (-3, 4).

Solution

The distance d between two points `(x_1, y_1)` and `(x_2, y_2)` is given by the formula

`d = sqrt((x_1-x_2)^2 + (y_1 - y_2)^2)`

Let the three given points be P(x, y), A(3,6) and B(3,4).

Now let us find the distance between ‘P’ and ‘A’.

`PA = sqrt((x - 3)^2 + (y - 3))`

Now, let us find the distance between ‘P’ and ‘B’.

`PB = sqrt((x + 3)^2 + (y - 6)^2)`

It is given that both these distances are equal. So, let us equate both the above equations,

PA = PB

`sqrt((x - 3)^2 + (y - 6)^2 )  = sqrt((x + 3)^2  + (y - 4)^2)`

Squaring on both sides of the equation we get

`(x - 3)^2 + (y - 6)^2 = (x + 3)^2 + (y - 4)^2`

`x^2 + 9 - 6x + y^2 + 36 - 12y = x62 + 9 + 6x + y^2 + 16 - 8y`

12x + 4y = 20

3x + y = 5

Hence the relationship between ‘x’ and ‘y’ based on the given condition is 3x + y = 5

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Solution Find a Relation Between X and Y Such that the Point (X, Y) is Equidistant from the Points (3, 6) and (−3, 4). Concept: Concepts of Coordinate Geometry.
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