{
"query": {
"display": "$$x^{2}+y^{2}\\le\\:25$$",
"symbolab_question": "CONIC#x^{2}+y^{2}\\le 25"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Circle",
"subTopic": "formula",
"default": "(a,b)=(0,0),r=5"
},
"steps": {
"type": "interim",
"title": "$$x^{2}+y^{2}\\le\\:25:\\quad$$Circle with center at $$\\left(0,\\:0\\right)\\:$$and radius $$r=5$$",
"input": "x^{2}+y^{2}\\le\\:25",
"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 $$x^{2}+y^{2}\\le\\:25\\:$$in the form of the standard circle equation",
"result": "\\left(x-0\\right)^{2}+\\left(y-0\\right)^{2}=5^{2}"
},
{
"type": "step",
"primary": "Therefore the circle properties are:",
"result": "\\left(a,\\:b\\right)=\\left(0,\\:0\\right),\\:r=5"
}
],
"meta": {
"solvingClass": "Circle"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"funcsToDraw": {
"funcs": [
{
"evalFormula": "y=\\sqrt{5^{2}-x^{2}}",
"displayFormula": "x^{2}+y^{2}=5^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
},
{
"evalFormula": "y=-\\sqrt{5^{2}-x^{2}}",
"displayFormula": "x^{2}+y^{2}=5^{2}",
"attributes": {
"color": "PURPLE",
"lineType": "NORMAL",
"isAsymptote": false
}
}
]
},
"pointsToDraw": {
"pointsLatex": [
"(0,0)"
],
"pointsDecimal": [
{
"fst": 0,
"snd": 0
}
],
"attributes": [
{
"color": "PURPLE",
"labels": [
"\\mathrm{Center}"
],
"labelTypes": [
"DEFAULT"
],
"labelColors": [
"PURPLE"
]
}
]
},
"linesToDraw": [
{
"p1x": "0",
"p1y": "0",
"p2x": "3.5355339059327",
"p2y": "3.5355339059327",
"attributes": {
"color": "GRAY",
"lineType": "BOLD",
"labels": [
"\\mathrm{radius=}5"
],
"isAsymptote": false
}
}
],
"fills": [
{
"ranges": [
{
"fst": "-5.0",
"snd": "5.0"
}
],
"funcIndices": [
{
"fst": 0,
"snd": 1
}
],
"funcs": [
{
"fst": "y=\\sqrt{5^{2}-x^{2}}",
"snd": "y=\\sqrt{5^{2}-x^{2}}"
}
],
"xIneq": false,
"yIneq": false,
"twoVar": false,
"trueAboveLine": false,
"color": "rgba(171, 181, 235, 0.3)"
}
],
"functionChanges": [
{
"origFormulaLatex": [],
"finalFormulaLatex": [],
"plotTitle": "x^{2}+y^{2}\\le 5^{2}",
"paramsLatex": [],
"paramsReplacementsLatex": []
}
],
"localBoundingBox": {
"xMin": -11.25,
"xMax": 11.25,
"yMin": -11.25,
"yMax": 11.25
}
},
"showViewLarger": true
}
}
}
Solution
Solution
Solution steps
Rewrite in the form of the standard circle equation
Therefore the circle properties are:
Graph
Popular Examples
2x^2+y^2=2(x-3)^2+y^2=4directrix y=-4x^2directrix vertices (x^2}{25}-\frac{y^2)/9 =1vertices x^2-2x-4y+9=0
Frequently Asked Questions (FAQ)
What is x^2+y^2<= 25 ?
The solution to x^2+y^2<= 25 is Circle with (a,b)=(0,0),r=5