Solve y^2=2px(1+lambda(1-6)

$$y ^ { 2 } = 2 p x ( 1 + \lambda ( 1 - 6 )$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{y^{2}}{2x\left(1-5\lambda \right)}\text{, }&\lambda \neq \frac{1}{5}\text{ and }x\neq 0\\p\in \mathrm{C}\text{, }&\left(x=0\text{ or }\lambda =\frac{1}{5}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6 from 1 to get -5.

$$y^{2}=2px\left(1+\lambda \left(-5\right)\right)$$

Use the distributive property to multiply 2px by 1+\lambda \left(-5\right).

$$y^{2}=2px-10\lambda px$$

Swap sides so that all variable terms are on the left hand side.

$$2px-10\lambda px=y^{2}$$

Combine all terms containing p.

$$\left(2x-10\lambda x\right)p=y^{2}$$

The equation is in standard form.

$$\left(2x-10x\lambda \right)p=y^{2}$$

Divide both sides by -10x\lambda +2x.

$$\frac{\left(2x-10x\lambda \right)p}{2x-10x\lambda }=\frac{y^{2}}{2x-10x\lambda }$$

Dividing by -10x\lambda +2x undoes the multiplication by -10x\lambda +2x.

$$p=\frac{y^{2}}{2x-10x\lambda }$$

Divide y^{2} by -10x\lambda +2x.

$$p=\frac{y^{2}}{2x\left(1-5\lambda \right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y^{2}}{2p\left(1-5\lambda \right)}\text{, }&\lambda \neq \frac{1}{5}\text{ and }p\neq 0\\x\in \mathrm{C}\text{, }&\left(p=0\text{ or }\lambda =\frac{1}{5}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6 from 1 to get -5.

$$y^{2}=2px\left(1+\lambda \left(-5\right)\right)$$

Use the distributive property to multiply 2px by 1+\lambda \left(-5\right).

$$y^{2}=2px-10\lambda px$$

Swap sides so that all variable terms are on the left hand side.

$$2px-10\lambda px=y^{2}$$

Combine all terms containing x.

$$\left(2p-10\lambda p\right)x=y^{2}$$

The equation is in standard form.

$$\left(2p-10p\lambda \right)x=y^{2}$$

Divide both sides by 2p-10p\lambda .

$$\frac{\left(2p-10p\lambda \right)x}{2p-10p\lambda }=\frac{y^{2}}{2p-10p\lambda }$$

Dividing by 2p-10p\lambda undoes the multiplication by 2p-10p\lambda .

$$x=\frac{y^{2}}{2p-10p\lambda }$$

Divide y^{2} by 2p-10p\lambda .

$$x=\frac{y^{2}}{2p\left(1-5\lambda \right)}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{y^{2}}{2x\left(1-5\lambda \right)}\text{, }&\lambda \neq \frac{1}{5}\text{ and }x\neq 0\\p\in \mathrm{R}\text{, }&\left(x=0\text{ or }\lambda =\frac{1}{5}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6 from 1 to get -5.

$$y^{2}=2px\left(1+\lambda \left(-5\right)\right)$$

Use the distributive property to multiply 2px by 1+\lambda \left(-5\right).

$$y^{2}=2px-10\lambda px$$

Swap sides so that all variable terms are on the left hand side.

$$2px-10\lambda px=y^{2}$$

Combine all terms containing p.

$$\left(2x-10\lambda x\right)p=y^{2}$$

The equation is in standard form.

$$\left(2x-10x\lambda \right)p=y^{2}$$

Divide both sides by -10x\lambda +2x.

$$\frac{\left(2x-10x\lambda \right)p}{2x-10x\lambda }=\frac{y^{2}}{2x-10x\lambda }$$

Dividing by -10x\lambda +2x undoes the multiplication by -10x\lambda +2x.

$$p=\frac{y^{2}}{2x-10x\lambda }$$

Divide y^{2} by -10x\lambda +2x.

$$p=\frac{y^{2}}{2x\left(1-5\lambda \right)}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y^{2}}{2p\left(1-5\lambda \right)}\text{, }&\lambda \neq \frac{1}{5}\text{ and }p\neq 0\\x\in \mathrm{R}\text{, }&\left(p=0\text{ or }\lambda =\frac{1}{5}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 6 from 1 to get -5.

$$y^{2}=2px\left(1+\lambda \left(-5\right)\right)$$

Use the distributive property to multiply 2px by 1+\lambda \left(-5\right).

$$y^{2}=2px-10\lambda px$$

Swap sides so that all variable terms are on the left hand side.

$$2px-10\lambda px=y^{2}$$

Combine all terms containing x.

$$\left(2p-10\lambda p\right)x=y^{2}$$

The equation is in standard form.

$$\left(2p-10p\lambda \right)x=y^{2}$$

Divide both sides by 2p-10p\lambda .

$$\frac{\left(2p-10p\lambda \right)x}{2p-10p\lambda }=\frac{y^{2}}{2p-10p\lambda }$$

Dividing by 2p-10p\lambda undoes the multiplication by 2p-10p\lambda .

$$x=\frac{y^{2}}{2p-10p\lambda }$$

Divide y^{2} by 2p-10p\lambda .

$$x=\frac{y^{2}}{2p\left(1-5\lambda \right)}$$