Solve (4)x^2+cy^2=1

$$( 4 ) x ^ { 2 } + c y ^ { 2 } = 1$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{1-4x^{2}}{y^{2}}\text{, }&y\neq 0\\c\in \mathrm{C}\text{, }&\left(x=-\frac{1}{2}\text{ or }x=\frac{1}{2}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x^{2} from both sides.

$$cy^{2}=1-4x^{2}$$

The equation is in standard form.

$$y^{2}c=1-4x^{2}$$

Divide both sides by y^{2}.

$$\frac{y^{2}c}{y^{2}}=\frac{1-4x^{2}}{y^{2}}$$

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

$$c=\frac{1-4x^{2}}{y^{2}}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{1-4x^{2}}{y^{2}}\text{, }&y\neq 0\\c\in \mathrm{R}\text{, }&y=0\text{ and }|x|=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4x^{2} from both sides.

$$cy^{2}=1-4x^{2}$$

The equation is in standard form.

$$y^{2}c=1-4x^{2}$$

Divide both sides by y^{2}.

$$\frac{y^{2}c}{y^{2}}=\frac{1-4x^{2}}{y^{2}}$$

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

$$c=\frac{1-4x^{2}}{y^{2}}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{1-cy^{2}}}{2}$$

$$x=\frac{\sqrt{1-cy^{2}}}{2}$$

Solve for x

$$x=\frac{\sqrt{1-cy^{2}}}{2}$$

$$x=-\frac{\sqrt{1-cy^{2}}}{2}\text{, }c\leq \frac{1}{y^{2}}\text{ or }y=0$$