Considere la ecuación de la circunferencia $\\simplify[all]{(x-{a})^2+(y-{b})^2}=\\simplify[basic]{{r}^2}$.
", "advice": "La intersección en el eje $x$ es el valor de $x$ cuando $y = 0$, es decir, el valor de $x$ donde la gráfica alcanza al eje $x$.
\nPara encontrar esto, sustituye $y=0$ en su ecuación:
\n\\[\\simplify[all]{(x-{a})^2}+\\simplify[basic]{(-{b})^2}={r}^2\\]
\ny resuelve para $x$:
\n| $\\simplify[all]{(x-{a})^2}$ | \n$=$ | \n$\\simplify[basic]{{r}^2-{abs(b)}^2}$ | \n
| $\\simplify[all]{(x-{a})}$ | \n$=$ | \n$\\pm\\sqrt{\\simplify[basic]{{r}^2-{abs(b)}^2}}$ | \n
| \n | $=$ | \n$\\pm\\sqrt{\\var{xdet}}$ | \n
| \n | $=$ | \n$\\pm$$\\var{xug}$ | \n
| $x$ | \n$=$ | \n$\\var{a}$$\\pm\\var{xug}$ | \n
| $x$ | \n$=$ | \n$\\var{a-xug}$$,\\var{a+xug}$ | \n
Si consideramos solo números reales, la raíz cuadrada de un número negativo no es un número real, no hay intersecciones en el eje $x$.
\nSi consideramos (mas o menos) la raíz cuadrada de cero solo tenemos una intersección con el eje $x$, $x=\\var{a}$.
\nEn este caso tenemos dos intersecciones en el eje $x$ distintas
\nLa intersección en el eje $y$ es el valor de $y$ cuando $x = 0$, es decir, el valor de $y$ donde la gráfica alcanza al eje $y$.
\n\nPara encontrar esto, reemplazamos $x=0$ sobre la ecuación:
\n\\[\\simplify[basic]{(-{a})^2}+\\simplify[all]{(y-{b})^2}=\\simplify[basic]{{r}^2}\\]
\ny resuelve para $y$:
\n| $\\simplify[all]{(y-{b})^2}$ | \n$=$ | \n$\\simplify[basic]{{r}^2-{abs(a)}^2}$ | \n
| $\\simplify[all]{(y-{b})}$ | \n$=$ | \n$\\pm\\sqrt{\\simplify[basic]{{r}^2-{abs(a)}^2}}$ | \n
| \n | $=$ | \n$\\pm\\sqrt{\\var{ydet}}$ | \n
| \n | $=$ | \n$\\pm$$\\var{yug}$ | \n
| $y$ | \n$=$ | \n$\\var{b}$$\\pm\\var{yug}$ | \n
| $y$ | \n$=$ | \n$\\var{b-yug}$$,\\var{b+yug}$ | \n
Si trabajamos con números reales, la raíz cuadrada de un número negativo no es real, no existe intersección en el eje $y$.
\nSi consideramos (más o menos) la raíz cuadrada de cero, solo tenemos una intersección en el eje $y$, $y=\\var{b}$.
\nEn este caso tenemos dos intersecciones - distintas - en el eje $y$.
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\nIndicación:
\nSi no existe intersección, ingrese sólo set()
\nSi existe una intersección, por ejemplo $x=5$, ingrese set(5)
\nSi existen dos intersecciones, por ejemplo $x=-2$ y $x=1.5$, ingrese set(-2,1.5)
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\nIndicación:
\nSi no existe intersección, ingrese set()
\nSi existe solo una intersección, por ejemplo $y=5$, ingrese set(5)
\nSi existen dos intersecciones, por ejemplo $y=-2$ y $y=1.5$, ingrese set(-2,1.5)
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