Whakaoti i te l/r=1+ecosθ

$$\frac { l } { r } = 1 + e \cos \theta$$

Whakaoti mō l

$$l=r\left(e\cos(\theta )+1\right)$$

$$r\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

He hanga arowhānui tō te whārite.

$$\frac{1}{r}l=e\cos(\theta )+1$$

Whakawehea ngā taha e rua ki te r^{-1}.

$$\frac{\frac{1}{r}lr}{1}=\frac{\left(e\cos(\theta )+1\right)r}{1}$$

Mā te whakawehe ki te r^{-1} ka wetekia te whakareanga ki te r^{-1}.

$$l=\frac{\left(e\cos(\theta )+1\right)r}{1}$$

Whakawehe 1+e\cos(\theta ) ki te r^{-1}.

$$l=r\left(e\cos(\theta )+1\right)$$

Whakaoti mō r

$$\left\{\begin{matrix}r=\frac{l}{e\cos(\theta )+1}\text{, }&l\neq 0\text{ and }\nexists n_{2}\in \mathrm{Z}\text{ : }\theta =2\pi n_{2}+\arccos(\frac{1}{e})+\pi \text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}-\arccos(\frac{1}{e})+\pi \\r\neq 0\text{, }&\left(\exists n_{4}\in \mathrm{Z}\text{ : }\theta =2\pi n_{4}+\arccos(\frac{1}{e})+\pi \text{ or }\exists n_{3}\in \mathrm{Z}\text{ : }\theta =2\pi n_{3}-\arccos(\frac{1}{e})+\pi \right)\text{ and }l=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe r ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te r.

$$l=r+e\cos(\theta )r$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$r+e\cos(\theta )r=l$$

Pahekotia ngā kīanga tau katoa e whai ana i te r.

$$\left(1+e\cos(\theta )\right)r=l$$

He hanga arowhānui tō te whārite.

$$\left(e\cos(\theta )+1\right)r=l$$

Whakawehea ngā taha e rua ki te 1+e\cos(\theta ).

$$\frac{\left(e\cos(\theta )+1\right)r}{e\cos(\theta )+1}=\frac{l}{e\cos(\theta )+1}$$

Mā te whakawehe ki te 1+e\cos(\theta ) ka wetekia te whakareanga ki te 1+e\cos(\theta ).

$$r=\frac{l}{e\cos(\theta )+1}$$

Tē taea kia ōrite te tāupe r ki 0.

$$r=\frac{l}{e\cos(\theta )+1}\text{, }r\neq 0$$