## Zenmo one year ago Eliminate the parameter and obtain the standard form of the rectangular equation.

1. Zenmo

Line through $(x _{1},y _{1}) and (x _{2},y _{2}): x=x _{1}+t(_{x2}-_{x1}), y=y _{1}+t(y _{2}-y _{1})$

2. Zenmo

Circle: $x=h+r \cos \theta, y=k+r \sin \theta$

3. anonymous

For the first, you can eliminate $$t$$ by solving for it in one of the equations, then substituting the resulting expression into the other equation. For example, take the first equation and you have $x=x_1+\color{red}t(x_2-x_1)~~\iff~~\color{red}t=\frac{x-x_1}{x_2-x_1}$and go from there. For the second, you can use a fundamental trigonometric identity. Recall that $$\cos^2\theta+\sin^2\theta=1$$. $\begin{cases}x-h=r\cos\theta\\y-k=r\sin\theta\end{cases}~~\implies~~\begin{cases}(x-h)^2=\mathbin{?}\\(y-k)^2=\mathbin{?}\end{cases}~~\implies~~(x-h)^2+(y-k)^2=\mathbin{?}$