(sqrt(x^2+y^2+100x+2500))-(sqrt(x^2+y^2-100x+2500))=60

Answer 1

√(x^2+y^2+100x+2500)-√(x^2+y^2-100x+2500) = 60

(x^2+y^2+100x+2500)-2√((x^2+y^2+100x+2500)(x^2+y^2-100x+2500))+(x^2+y^2-100x+2500) = 3600

2(x^2+y^2+2500) - 2√(x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000) = 3600

√(x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000) = x^2+y^2+700
x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000 = x^4+2x^2y^2+y^4+1400x^2+1400y^2+490000

-5000x^2+5000y^2+6250000 = 1400x^2+1400y^2+490000

-6400x^2+3600y^2+5760000 = 0
64x^2-36y^2 = 57600
x^2/900 - y^2/1600 = 1

That's just an hyperbola with vertices at (±30,0)