Whakaoti i te x(x-a)+y(y-c)=0

$$x ( x - a ) + y ( y - c ) = 0$$

Whakaoti mō a (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te y ki te y-c.

$$x^{2}-xa+y^{2}-yc=0$$

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-xa+y^{2}-yc=-x^{2}$$

Tangohia te y^{2} mai i ngā taha e rua.

$$-xa-yc=-x^{2}-y^{2}$$

Me tāpiri te yc ki ngā taha e rua.

$$-xa=-x^{2}-y^{2}+yc$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)a=cy-y^{2}-x^{2}$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)a}{-x}=\frac{cy-y^{2}-x^{2}}{-x}$$

Mā te whakawehe ki te -x ka wetekia te whakareanga ki te -x.

$$a=\frac{cy-y^{2}-x^{2}}{-x}$$

Whakawehe -x^{2}-y^{2}+cy ki te -x.

$$a=\frac{y^{2}-cy}{x}+x$$

Whakaoti mō c (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te y ki te y-c.

$$x^{2}-xa+y^{2}-yc=0$$

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-xa+y^{2}-yc=-x^{2}$$

Me tāpiri te xa ki ngā taha e rua.

$$y^{2}-yc=-x^{2}+xa$$

Tangohia te y^{2} mai i ngā taha e rua.

$$-yc=-x^{2}+xa-y^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-y\right)c=ax-y^{2}-x^{2}$$

Whakawehea ngā taha e rua ki te -y.

$$\frac{\left(-y\right)c}{-y}=\frac{ax-y^{2}-x^{2}}{-y}$$

Mā te whakawehe ki te -y ka wetekia te whakareanga ki te -y.

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

Whakawehe -x^{2}-y^{2}+xa ki te -y.

$$c=\frac{x^{2}-ax}{y}+y$$

Whakaoti mō a

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te y ki te y-c.

$$x^{2}-xa+y^{2}-yc=0$$

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-xa+y^{2}-yc=-x^{2}$$

Tangohia te y^{2} mai i ngā taha e rua.

$$-xa-yc=-x^{2}-y^{2}$$

Me tāpiri te yc ki ngā taha e rua.

$$-xa=-x^{2}-y^{2}+yc$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)a=cy-y^{2}-x^{2}$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)a}{-x}=\frac{cy-y^{2}-x^{2}}{-x}$$

Mā te whakawehe ki te -x ka wetekia te whakareanga ki te -x.

$$a=\frac{cy-y^{2}-x^{2}}{-x}$$

Whakawehe -x^{2}-y^{2}+yc ki te -x.

$$a=\frac{y^{2}-cy}{x}+x$$

Whakaoti mō c

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-a.

$$x^{2}-xa+y\left(y-c\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te y ki te y-c.

$$x^{2}-xa+y^{2}-yc=0$$

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-xa+y^{2}-yc=-x^{2}$$

Me tāpiri te xa ki ngā taha e rua.

$$y^{2}-yc=-x^{2}+xa$$

Tangohia te y^{2} mai i ngā taha e rua.

$$-yc=-x^{2}+xa-y^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-y\right)c=ax-y^{2}-x^{2}$$

Whakawehea ngā taha e rua ki te -y.

$$\frac{\left(-y\right)c}{-y}=\frac{ax-y^{2}-x^{2}}{-y}$$

Mā te whakawehe ki te -y ka wetekia te whakareanga ki te -y.

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

Whakawehe -x^{2}+xa-y^{2} ki te -y.

$$c=\frac{x^{2}-ax}{y}+y$$