Question

If the distance of p(x,y) from A(5,1) and B(-15) are equal then prove that 3x=2y.

Answer 1

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Answer 2

Distance of p(x,y) from A(5,1) and B(-1,5) are equal and 3x = 2y is proven.

Solution:

Distance from point x, y to A (5, 1) and B(-1, 5) is same which can be proven by finding the distance between the points given.

To prove:  3x = 2y

Considering AZ = ZB, that means $A Z^{2}=Z B^{2}$

$(x-5)^{2}+(y-1)^{2}=(x+1)^{2}+(y-5)^{2}$

Squaring both the sides we get the factors and then simplifying them we get:

$x^{2}+25-10 x+y^{2}+1-2 y=x^{2}+1+2 x+y^{2}+25-10 y$

12x = 8y

3x = 2y  

Hence proved.