{
"query": {
"display": "$$\\left(x-1\\right)^{2}+y^{2}=1$$",
"symbolab_question": "CONIC#(x-1)^{2}+y^{2}=1"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Circle",
"subTopic": "formula",
"default": "(a,b)=(1,0),r=1"
},
"steps": {
"type": "interim",
"title": "$$\\left(x-1\\right)^{2}+y^{2}=1:\\quad$$Circunferencia con centro en $$\\left(1,\\:0\\right)\\:$$y radio $$r=1$$",
"input": "\\left(x-1\\right)^{2}+y^{2}=1",
"steps": [
{
"type": "definition",
"title": "Ecuación del circulo",
"text": "$$\\left(x−a\\right)^2+\\left(y−b\\right)^2=r^2\\:\\:$$es la ecuación del circulo con radio r, con centro en $$\\left(a,\\:b\\right)$$"
},
{
"type": "step",
"primary": "Reescribir $$\\left(x-1\\right)^{2}+y^{2}=1\\:$$con la forma de la ecuación ordinaria de la circunferencia",
"result": "\\left(x-1\\right)^{2}+\\left(y-0\\right)^{2}=1^{2}"
},
{
"type": "step",
"primary": "Por lo tanto, las propiedades del circulo son:",
"result": "\\left(a,\\:b\\right)=\\left(1,\\:0\\right),\\:r=1"
}
],
"meta": {
"solvingClass": "Circle"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"funcsToDraw": {
"funcs": [
{
"evalFormula": "y=\\sqrt{1^{2}-(x-1)^{2}}",
"displayFormula": "(x-1)^{2}+y^{2}=1^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
},
{
"evalFormula": "y=-\\sqrt{1^{2}-(x-1)^{2}}",
"displayFormula": "(x-1)^{2}+y^{2}=1^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
}
]
},
"pointsToDraw": {
"pointsLatex": [
"(1,0)"
],
"pointsDecimal": [
{
"fst": 1,
"snd": 0
}
],
"attributes": [
{
"color": "PURPLE",
"labels": [
"\\mathrm{Center}"
],
"labelTypes": [
"DEFAULT"
],
"labelColors": [
"PURPLE"
]
}
]
},
"linesToDraw": [
{
"p1x": "1",
"p1y": "0",
"p2x": "1.7071067811865",
"p2y": "0.7071067811865",
"attributes": {
"color": "GRAY",
"lineType": "BOLD",
"labels": [
"\\mathrm{radius=}1"
],
"isAsymptote": false
}
}
],
"functionChanges": [
{
"origFormulaLatex": [],
"finalFormulaLatex": [],
"plotTitle": "(x-1)^{2}+y^{2}=1^{2}",
"paramsLatex": [],
"paramsReplacementsLatex": []
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"localBoundingBox": {
"xMin": -1.4071428571428573,
"xMax": 3.0928571428571425,
"yMin": -2.25,
"yMax": 2.25
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"showViewLarger": true
}
}
}
Solución
Solución
Pasos de solución
Reescribir con la forma de la ecuación ordinaria de la circunferencia
Por lo tanto, las propiedades del circulo son: