Whakaoti i te {l}{x^2/4+y^2=1}{y=frac{sqrt{2}}{4}x}

$$\left. \begin{array} { l } { \frac { x ^ { 2 } } { 4 } + y ^ { 2 } = 1 } \\ { y = \frac { \sqrt { 2 } } { 4 } x } \end{array} \right.$$

Whakaoti mō x, y

$$x=-\frac{2\sqrt{6}}{3}\approx -1.632993162\text{, }y=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

$$x=\frac{2\sqrt{6}}{3}\approx 1.632993162\text{, }y=\frac{\sqrt{3}}{3}\approx 0.577350269$$

Ngā Upane e Whakamahi ana i te Whakakapinga me te Tikanga Tātai Pūrua

Whakaarohia te whārite tuatahi. Whakareatia ngā taha e rua o te whārite ki te 4.

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

Whakaarohia te whārite tuarua. Tuhia te \frac{\sqrt{2}}{4}x hei hautanga kotahi.

$$y=\frac{\sqrt{2}x}{4}$$

Tangohia te \frac{\sqrt{2}x}{4} mai i ngā taha e rua.

$$y-\frac{\sqrt{2}x}{4}=0$$

Whakareatia ngā taha e rua o te whārite ki te 4.

$$4y-\sqrt{2}x=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-\sqrt{2}x+4y=0$$

Hei whakaoti i ētahi whārite takirua mā te whakakapinga, me whakaoti tētahi whārite i te tuatahi mō tētahi o ngā taurangi. Ka whakakapi i te otinga mō taua taurangi ki tērā o ngā whārite.

$$\left(-\sqrt{2}\right)x+4y=0,4y^{2}+x^{2}=4$$

Whakaotia te \left(-\sqrt{2}\right)x+4y=0 mō x mā te wehe i te x i te taha mauī o te tohu ōrite.

$$\left(-\sqrt{2}\right)x+4y=0$$

Me tango 4y mai i ngā taha e rua o te whārite.

$$\left(-\sqrt{2}\right)x=-4y$$

Whakawehea ngā taha e rua ki te -\sqrt{2}.

$$x=2\sqrt{2}y$$

Whakakapia te 2\sqrt{2}y mō te x ki tērā atu whārite, 4y^{2}+x^{2}=4.

$$4y^{2}+\left(2\sqrt{2}y\right)^{2}=4$$

Pūrua 2\sqrt{2}y.

$$4y^{2}+\left(2\sqrt{2}\right)^{2}y^{2}=4$$

Tāpiri 4y^{2} ki te \left(2\sqrt{2}\right)^{2}y^{2}.

$$\left(\left(2\sqrt{2}\right)^{2}+4\right)y^{2}=4$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$\left(\left(2\sqrt{2}\right)^{2}+4\right)y^{2}-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4+1\times \left(2\sqrt{2}\right)^{2} mō a, 1\times 0\times 2\times 2\sqrt{2} mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(\left(2\sqrt{2}\right)^{2}+4\right)\left(-4\right)}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Pūrua 1\times 0\times 2\times 2\sqrt{2}.

$$y=\frac{0±\sqrt{-4\left(\left(2\sqrt{2}\right)^{2}+4\right)\left(-4\right)}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Whakareatia -4 ki te 4+1\times \left(2\sqrt{2}\right)^{2}.

$$y=\frac{0±\sqrt{-48\left(-4\right)}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Whakareatia -48 ki te -4.

$$y=\frac{0±\sqrt{192}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Tuhia te pūtakerua o te 192.

$$y=\frac{0±8\sqrt{3}}{2\left(\left(2\sqrt{2}\right)^{2}+4\right)}$$

Whakareatia 2 ki te 4+1\times \left(2\sqrt{2}\right)^{2}.

$$y=\frac{0±8\sqrt{3}}{24}$$

Nā, me whakaoti te whārite y=\frac{0±8\sqrt{3}}{24} ina he tāpiri te ±.

$$y=\frac{\sqrt{3}}{3}$$

Nā, me whakaoti te whārite y=\frac{0±8\sqrt{3}}{24} ina he tango te ±.

$$y=-\frac{\sqrt{3}}{3}$$

E rua ngā otinga mō y: \frac{\sqrt{3}}{3} me -\frac{\sqrt{3}}{3}. Me whakakapi \frac{\sqrt{3}}{3} mō y ki te whārite x=2\sqrt{2}y hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=2\sqrt{2}\times \frac{\sqrt{3}}{3}$$

Me whakakapi te -\frac{\sqrt{3}}{3} ināianei mō te y ki te whārite x=2\sqrt{2}y ka whakaoti hei kimi i te otinga hāngai mō x e pai ai ki ngā whārite e rua.

$$x=2\sqrt{2}\left(-\frac{\sqrt{3}}{3}\right)$$

Kua oti te pūnaha te whakatau.

$$x=2\sqrt{2}\times \frac{\sqrt{3}}{3},y=\frac{\sqrt{3}}{3}\text{ or }x=2\sqrt{2}\left(-\frac{\sqrt{3}}{3}\right),y=-\frac{\sqrt{3}}{3}$$