Solve C:x^2/m-y^2=1

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

Solve for m (complex solution)

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

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Divide C by \frac{x^{2}}{m} by multiplying C by the reciprocal of \frac{x^{2}}{m}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2} times \frac{x^{2}}{x^{2}}.

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

Since \frac{Cm}{x^{2}} and \frac{y^{2}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Multiply both sides of the equation by x^{2}.

$$Cm-y^{2}x^{2}=x^{2}$$

Add y^{2}x^{2} to both sides.

$$Cm=x^{2}+y^{2}x^{2}$$

The equation is in standard form.

$$Cm=x^{2}y^{2}+x^{2}$$

Divide both sides by C.

$$\frac{Cm}{C}=\frac{\left(y-i\right)\left(y+i\right)x^{2}}{C}$$

Dividing by C undoes the multiplication by C.

$$m=\frac{\left(y-i\right)\left(y+i\right)x^{2}}{C}$$

Variable m cannot be equal to 0.

$$m=\frac{\left(y-i\right)\left(y+i\right)x^{2}}{C}\text{, }m\neq 0$$

Solve for C

$$C=\frac{x^{2}\left(y^{2}+1\right)}{m}$$

$$x\neq 0\text{ and }m\neq 0$$

Steps for Solving Linear Equation

Divide C by \frac{x^{2}}{m} by multiplying C by the reciprocal of \frac{x^{2}}{m}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2} times \frac{x^{2}}{x^{2}}.

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

Since \frac{Cm}{x^{2}} and \frac{y^{2}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Multiply both sides of the equation by x^{2}.

$$Cm-y^{2}x^{2}=x^{2}$$

Add y^{2}x^{2} to both sides.

$$Cm=x^{2}+y^{2}x^{2}$$

The equation is in standard form.

$$mC=x^{2}y^{2}+x^{2}$$

Divide both sides by m.

$$\frac{mC}{m}=\frac{x^{2}\left(y^{2}+1\right)}{m}$$

Dividing by m undoes the multiplication by m.

$$C=\frac{x^{2}\left(y^{2}+1\right)}{m}$$

Solve for m

$$m=\frac{x^{2}\left(y^{2}+1\right)}{C}$$

$$x\neq 0\text{ and }C\neq 0$$

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Divide C by \frac{x^{2}}{m} by multiplying C by the reciprocal of \frac{x^{2}}{m}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply y^{2} times \frac{x^{2}}{x^{2}}.

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

Since \frac{Cm}{x^{2}} and \frac{y^{2}x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Multiply both sides of the equation by x^{2}.

$$Cm-y^{2}x^{2}=x^{2}$$

Add y^{2}x^{2} to both sides.

$$Cm=x^{2}+y^{2}x^{2}$$

The equation is in standard form.

$$Cm=x^{2}y^{2}+x^{2}$$

Divide both sides by C.

$$\frac{Cm}{C}=\frac{x^{2}\left(y^{2}+1\right)}{C}$$

Dividing by C undoes the multiplication by C.

$$m=\frac{x^{2}\left(y^{2}+1\right)}{C}$$

Variable m cannot be equal to 0.

$$m=\frac{x^{2}\left(y^{2}+1\right)}{C}\text{, }m\neq 0$$