Whakaoti i te (x-2)^2+(y-2)^2=1(x-(-2))^2+(y-4)

$$( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 1 ( x - ( - 2 ) ) ^ { 2 } + ( y - 4 )$$

Whakaoti mō x

$$x=\frac{y^{2}-5y+8}{8}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

$$x^{2}-4x+4+\left(y-2\right)^{2}=1\left(x-\left(-2\right)\right)^{2}+y-4$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(y-2\right)^{2}.

$$x^{2}-4x+4+y^{2}-4y+4=1\left(x-\left(-2\right)\right)^{2}+y-4$$

Tāpirihia te 4 ki te 4, ka 8.

$$x^{2}-4x+8+y^{2}-4y=1\left(x-\left(-2\right)\right)^{2}+y-4$$

Ko te tauaro o -2 ko 2.

$$x^{2}-4x+8+y^{2}-4y=1\left(x+2\right)^{2}+y-4$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+2\right)^{2}.

$$x^{2}-4x+8+y^{2}-4y=1\left(x^{2}+4x+4\right)+y-4$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1 ki te x^{2}+4x+4.

$$x^{2}-4x+8+y^{2}-4y=x^{2}+4x+4+y-4$$

Tangohia te 4 i te 4, ka 0.

$$x^{2}-4x+8+y^{2}-4y=x^{2}+4x+y$$

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

$$x^{2}-4x+8+y^{2}-4y-x^{2}=4x+y$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$-4x+8+y^{2}-4y=4x+y$$

Tangohia te 4x mai i ngā taha e rua.

$$-4x+8+y^{2}-4y-4x=y$$

Pahekotia te -4x me -4x, ka -8x.

$$-8x+8+y^{2}-4y=y$$

Tangohia te 8 mai i ngā taha e rua.

$$-8x+y^{2}-4y=y-8$$

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

$$-8x-4y=y-8-y^{2}$$

Me tāpiri te 4y ki ngā taha e rua.

$$-8x=y-8-y^{2}+4y$$

Pahekotia te y me 4y, ka 5y.

$$-8x=5y-8-y^{2}$$

He hanga arowhānui tō te whārite.

$$-8x=-y^{2}+5y-8$$

Whakawehea ngā taha e rua ki te -8.

$$\frac{-8x}{-8}=\frac{-y^{2}+5y-8}{-8}$$

Mā te whakawehe ki te -8 ka wetekia te whakareanga ki te -8.

$$x=\frac{-y^{2}+5y-8}{-8}$$

Whakawehe 5y-8-y^{2} ki te -8.

$$x=\frac{y^{2}}{8}-\frac{5y}{8}+1$$

Whakaoti mō y (complex solution)

$$y=\frac{\sqrt{32x-7}+5}{2}$$

$$y=\frac{-\sqrt{32x-7}+5}{2}$$

Whakaoti mō y

$$y=\frac{\sqrt{32x-7}+5}{2}$$

$$y=\frac{-\sqrt{32x-7}+5}{2}\text{, }x\geq \frac{7}{32}$$