Analytical geometry!

Plz answer before tommorow, I really need this answer!

A point P moves such that the sum of its distances from points (4,0) and (-4,0)is 10. Prove that the equation of locus of P is x^2/25 + y^2/9 = 1

according to ur question,
sqrt{(x-4)^2+y^2} + sqrt{(x+4)^2+y^2}= 10 ......sqrt stands for square root
sqrt{(x-4)^2+y^2} = 10-sqrt{(x+4)^2+y^2}
squaring both sides,
(x-4)^2+y^2= 100+(x+4)^2+y^2-20*sqrt{(x+4)^2+y^2}
simplifying we get,
16*x+100= 20*sqrt{(x+4)^2+y^2}
8*x+50= 10*sqrt{(x+4)^2+y^2}
squaring both sides,
64*x^2+2500+800*x= 100*x^2+100*y^2+800*x+1600
simplifying we get,
36*x^2+100*y^2= 900
x^2/25 + y^2/9 = 1 ........................PROVED

@jessie: u r always welcome..

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