Question

Forma explícita da curva -2x²y+y²=1

Answer 1

Resposta:

-2x²y+y²=1

y²-2x²y-1=0   [é uma eq. do 2ª grau, podemos resolver normalmente]

y²-2x²y-1=0   ==>a=1,  b=-2x²  e   c =-1

y(x)=[2x²±√(4x⁴+4]/2

y(x)=[2x²±2√(x⁴+1]/2

y(x)= x²±√(x⁴+1 )          

Answer 2

$\mathsf{-2{x}^{2}y+{y}^{2}=1\times(-1)}\\\mathsf{2{x}^{2}y-{y}^{2}=-1}\\\mathsf{2{x}^{2}y={y}^{2}-1}$

$\mathsf{{x}^{2}=\dfrac{{y}^{2}}{2y}-\dfrac{1}{2y}}$

$\mathsf{{x}^{2}=\dfrac{{y}^{2}-1}{2y}}$

$\boxed{\boxed{\mathsf{x=\pm\sqrt{\dfrac{{y}^{2}-1}{2y} \: \: \: y\ne0}}}}$