Datrys {l}{-y_{1}(x_{1}+g)=(x-x_{1})(y_{1}+f).text{isa}}{text{Thepoint}P(x_{1},y_{1})text{liesoutside,on}}{y^2+2gx+2fy+c=0text{accordingas}}

$$\left. \begin{array} { l } { - y _ { 1 } ( x _ { 1 } + g ) = ( x - x _ { 1 } ) ( y _ { 1 } + f ) . \text { is a } } \\ { \text { The point } P ( x _ { 1 } , y _ { 1 } ) \text { lies outside, on } } \\ { y ^ { 2 } + 2 g x + 2 f y + c = 0 \text { according as } } \end{array} \right.$$

Datrys ar gyfer x (complex solution)

$$\left\{\begin{matrix}x=-\frac{gy_{1}-fx_{1}}{y_{1}+f}\text{, }&y_{1}\neq -f\\x\in \mathrm{C}\text{, }&\left(y_{1}=0\text{ and }f=0\right)\text{ or }\left(x_{1}=-g\text{ and }y_{1}=-f\right)\end{matrix}\right.$$

Camau ar gyfer Datrys Hafaliad Llinol

Defnyddio’r briodwedd ddosbarthu i luosi -y_{1} â x_{1}+g.

$$\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g=\left(x-x_{1}\right)\left(y_{1}+f\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x-x_{1} â y_{1}+f.

$$\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g=xy_{1}+xf-x_{1}y_{1}-x_{1}f$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$xy_{1}+xf-x_{1}y_{1}-x_{1}f=\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g$$

Ychwanegu x_{1}y_{1} at y ddwy ochr.

$$xy_{1}+xf-x_{1}f=\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g+x_{1}y_{1}$$

Ychwanegu x_{1}f at y ddwy ochr.

$$xy_{1}+xf=\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g+x_{1}y_{1}+x_{1}f$$

Cyfuno -y_{1}x_{1} a x_{1}y_{1} i gael 0.

$$xy_{1}+xf=-y_{1}g+x_{1}f$$

Cyfuno pob term sy'n cynnwys x.

$$\left(y_{1}+f\right)x=-y_{1}g+x_{1}f$$

Mae'r hafaliad yn y ffurf safonol.

$$\left(y_{1}+f\right)x=fx_{1}-gy_{1}$$

Rhannu’r ddwy ochr â y_{1}+f.

$$\frac{\left(y_{1}+f\right)x}{y_{1}+f}=\frac{fx_{1}-gy_{1}}{y_{1}+f}$$

Mae rhannu â y_{1}+f yn dad-wneud lluosi â y_{1}+f.

$$x=\frac{fx_{1}-gy_{1}}{y_{1}+f}$$

Datrys ar gyfer x

$$\left\{\begin{matrix}x=-\frac{gy_{1}-fx_{1}}{y_{1}+f}\text{, }&y_{1}\neq -f\\x\in \mathrm{R}\text{, }&\left(y_{1}=0\text{ and }f=0\right)\text{ or }\left(x_{1}=-g\text{ and }y_{1}=-f\right)\end{matrix}\right.$$

Camau ar gyfer Datrys Hafaliad Llinol

Defnyddio’r briodwedd ddosbarthu i luosi -y_{1} â x_{1}+g.

$$\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g=\left(x-x_{1}\right)\left(y_{1}+f\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x-x_{1} â y_{1}+f.

$$\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g=xy_{1}+xf-x_{1}y_{1}-x_{1}f$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$xy_{1}+xf-x_{1}y_{1}-x_{1}f=\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g$$

Ychwanegu x_{1}y_{1} at y ddwy ochr.

$$xy_{1}+xf-x_{1}f=\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g+x_{1}y_{1}$$

Ychwanegu x_{1}f at y ddwy ochr.

$$xy_{1}+xf=\left(-y_{1}\right)x_{1}+\left(-y_{1}\right)g+x_{1}y_{1}+x_{1}f$$

Cyfuno -y_{1}x_{1} a x_{1}y_{1} i gael 0.

$$xy_{1}+xf=-y_{1}g+x_{1}f$$

Cyfuno pob term sy'n cynnwys x.

$$\left(y_{1}+f\right)x=-y_{1}g+x_{1}f$$

Mae'r hafaliad yn y ffurf safonol.

$$\left(y_{1}+f\right)x=fx_{1}-gy_{1}$$

Rhannu’r ddwy ochr â y_{1}+f.

$$\frac{\left(y_{1}+f\right)x}{y_{1}+f}=\frac{fx_{1}-gy_{1}}{y_{1}+f}$$

Mae rhannu â y_{1}+f yn dad-wneud lluosi â y_{1}+f.

$$x=\frac{fx_{1}-gy_{1}}{y_{1}+f}$$