Solve x^2+(y-1)(x)^2=1

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

Solve for y

$$y=\frac{1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply y-1 by x^{2}.

$$x^{2}+yx^{2}-x^{2}=1$$

Combine x^{2} and -x^{2} to get 0.

$$yx^{2}=1$$

The equation is in standard form.

$$x^{2}y=1$$

Divide both sides by x^{2}.

$$\frac{x^{2}y}{x^{2}}=\frac{1}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$y=\frac{1}{x^{2}}$$

Solve for x (complex solution)

$$x=-y^{-\frac{1}{2}}$$

$$x=y^{-\frac{1}{2}}\text{, }y\neq 0$$

Solve for x

$$x=\frac{1}{\sqrt{y}}$$

$$x=-\frac{1}{\sqrt{y}}\text{, }y>0$$