Find the values of x, y if the distances of the point


Find the values of x, y if the distances of the point (xy) from (−3, 0)  as well as from (3, 0) are 4.


The distance $d$ between two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by the formula


It is said that (x, y) is equidistant from both (−3,0) and (3,0).

Let  be the distance between (x, y) and (−3,0).

Let  be the distance between (x, y) and (3,0).

So, using the distance formula for both these pairs of points we have



Now since both these distances are given to be the same, let us equate both  and .



Squaring on both sides we have,


$x^{2}+9+6 x+y^{2}=x^{2}+9-6 x+y^{2}$

$12 x=0$


It is also said that the value of both  and  is 4 units.

Substituting the value of ‘x’ in the equation for either  or  we can get the value of ‘y’.





Squaring on both sides of the equation we have,



$y=\pm \sqrt{7}$

Hence the values of ' $x$ ' and ' $y$ ' are $x=0$

$y=\pm \sqrt{7}$ .


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