{
"query": {
"display": "$$y^{2}=4-x^{2}$$",
"symbolab_question": "CONIC#y^{2}=4-x^{2}"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Circle",
"subTopic": "formula",
"default": "(a,b)=(0,0),r=2"
},
"steps": {
"type": "interim",
"title": "$$y^{2}=4-x^{2}:\\quad$$Circle with center at $$\\left(0,\\:0\\right)\\:$$and radius $$r=2$$",
"input": "y^{2}=4-x^{2}",
"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 $$y^{2}=4-x^{2}\\:$$in the form of the standard circle equation",
"result": "\\left(x-0\\right)^{2}+\\left(y-0\\right)^{2}=2^{2}"
},
{
"type": "step",
"primary": "Therefore the circle properties are:",
"result": "\\left(a,\\:b\\right)=\\left(0,\\:0\\right),\\:r=2"
}
],
"meta": {
"solvingClass": "Circle"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"funcsToDraw": {
"funcs": [
{
"evalFormula": "y=\\sqrt{2^{2}-x^{2}}",
"displayFormula": "x^{2}+y^{2}=2^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
},
{
"evalFormula": "y=-\\sqrt{2^{2}-x^{2}}",
"displayFormula": "x^{2}+y^{2}=2^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
}
]
},
"pointsToDraw": {
"pointsLatex": [
"(0,0)"
],
"pointsDecimal": [
{
"fst": 0,
"snd": 0
}
],
"attributes": [
{
"color": "PURPLE",
"labels": [
"\\mathrm{Center}"
],
"labelTypes": [
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],
"labelColors": [
"PURPLE"
]
}
]
},
"linesToDraw": [
{
"p1x": "0",
"p1y": "0",
"p2x": "1.4142135623731",
"p2y": "1.4142135623731",
"attributes": {
"color": "GRAY",
"lineType": "BOLD",
"labels": [
"\\mathrm{radius=}2"
],
"isAsymptote": false
}
}
],
"functionChanges": [
{
"origFormulaLatex": [],
"finalFormulaLatex": [],
"plotTitle": "x^{2}+y^{2}=2^{2}",
"paramsLatex": [],
"paramsReplacementsLatex": []
}
],
"localBoundingBox": {
"xMin": -4.5,
"xMax": 4.5,
"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
asymptotes of (x^2)/4-(y^2)/4 =1asymptotes axis (x^2)/9-(y^2)/4 =1axis foci (y^2)/(36)-(x^2)/(64)=1foci x=y-y^2y^2-8x=0
Frequently Asked Questions (FAQ)
What is y^2=4-x^2 ?
The solution to y^2=4-x^2 is Circle with (a,b)=(0,0),r=2