{
"query": {
"display": "$$\\left(x-3\\right)^{2}+y^{2}=4$$",
"symbolab_question": "CONIC#(x-3)^{2}+y^{2}=4"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Circle",
"subTopic": "formula",
"default": "(a,b)=(3,0),r=2"
},
"steps": {
"type": "interim",
"title": "$$\\left(x-3\\right)^{2}+y^{2}=4:\\quad$$Circle with center at $$\\left(3,\\:0\\right)\\:$$and radius $$r=2$$",
"input": "\\left(x-3\\right)^{2}+y^{2}=4",
"steps": [
{
"type": "definition",
"title": "Circle Equation",
"text": "$$\\left(x−a\\right)^2+\\left(y−b\\right)^2=r^2\\:\\:$$is the circle equation with a radius r, centered at $$\\left(a,\\:b\\right)$$"
},
{
"type": "step",
"primary": "Rewrite $$\\left(x-3\\right)^{2}+y^{2}=4\\:$$in the form of the standard circle equation",
"result": "\\left(x-3\\right)^{2}+\\left(y-0\\right)^{2}=2^{2}"
},
{
"type": "step",
"primary": "Therefore the circle properties are:",
"result": "\\left(a,\\:b\\right)=\\left(3,\\:0\\right),\\:r=2"
}
],
"meta": {
"solvingClass": "Circle"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"funcsToDraw": {
"funcs": [
{
"evalFormula": "y=\\sqrt{2^{2}-(x-3)^{2}}",
"displayFormula": "(x-3)^{2}+y^{2}=2^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
},
{
"evalFormula": "y=-\\sqrt{2^{2}-(x-3)^{2}}",
"displayFormula": "(x-3)^{2}+y^{2}=2^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
}
]
},
"pointsToDraw": {
"pointsLatex": [
"(3,0)"
],
"pointsDecimal": [
{
"fst": 3,
"snd": 0
}
],
"attributes": [
{
"color": "PURPLE",
"labels": [
"\\mathrm{Center}"
],
"labelTypes": [
"DEFAULT"
],
"labelColors": [
"PURPLE"
]
}
]
},
"linesToDraw": [
{
"p1x": "3",
"p1y": "0",
"p2x": "4.4142135623731",
"p2y": "1.4142135623731",
"attributes": {
"color": "GRAY",
"lineType": "BOLD",
"labels": [
"\\mathrm{radius=}2"
],
"isAsymptote": false
}
}
],
"functionChanges": [
{
"origFormulaLatex": [],
"finalFormulaLatex": [],
"plotTitle": "(x-3)^{2}+y^{2}=2^{2}",
"paramsLatex": [],
"paramsReplacementsLatex": []
}
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"localBoundingBox": {
"xMin": -2.357142857142857,
"xMax": 6.642857142857142,
"yMin": -4.5,
"yMax": 4.5
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"showViewLarger": true
}
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}
Solution
Solution
Solution steps
Rewrite in the form of the standard circle equation
Therefore the circle properties are:
Graph
Popular Examples
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Frequently Asked Questions (FAQ)
What is (x-3)^2+y^2=4 ?
The solution to (x-3)^2+y^2=4 is Circle with (a,b)=(3,0),r=2