{
"query": {
"display": "$$\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1$$",
"symbolab_question": "CONIC#\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Ellipse",
"subTopic": "formula",
"default": "(h,k)=(0,0),a=4,b=2"
},
"steps": {
"type": "interim",
"title": "$$\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1:{\\quad}$$Ellipse with center $$\\left(h,\\:k\\right)=\\left(0,\\:0\\right),\\:a=4,\\:b=2$$",
"input": "\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1",
"steps": [
{
"type": "definition",
"title": "Ellipse standard equation",
"text": "$$\\frac{\\left(x-h\\right)^{2}}{a^2}+\\frac{\\left(y-k\\right)^{2}}{b^2}=1\\:$$is the ellipse standard equation<br/>with center $$\\left(h,\\:k\\right)\\:$$and $$a,\\:b$$ are the semi-major and semi-minor axes"
},
{
"type": "step",
"primary": "Rewrite $$\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1\\:$$in the form of the standard ellipse equation",
"result": "\\frac{\\left(x-0\\right)^{2}}{4^{2}}+\\frac{\\left(y-0\\right)^{2}}{2^{2}}=1"
},
{
"type": "step",
"primary": "Therefore ellipse properties are:",
"result": "\\left(h,\\:k\\right)=\\left(0,\\:0\\right),\\:a=4,\\:b=2"
},
{
"type": "step",
"primary": "$$a>b\\:$$therefore $$a\\:$$is semi-major axis and $$b\\:$$is semi-minor axis",
"result": "\\mathrm{Ellipse\\:with\\:center}\\:\\left(h,\\:k\\right)=\\left(0,\\:0\\right),\\:a=4,\\:b=2"
}
],
"meta": {
"solvingClass": "Ellipse"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "x",
"funcsToDraw": {
"funcs": [
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"evalFormula": "y=\\sqrt{4(1-\\frac{x^{2}}{4^{2}})}",
"displayFormula": "\\frac{x^{2}}{4^{2}}+\\frac{y^{2}}{2^{2}}=1",
"attributes": {
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"evalFormula": "y=-\\sqrt{4(1-\\frac{x^{2}}{4^{2}})}",
"displayFormula": "\\frac{x^{2}}{4^{2}}+\\frac{y^{2}}{2^{2}}=1",
"attributes": {
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"attributes": [
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"color": "PURPLE",
"labels": [
"\\mathrm{Center}"
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"labelTypes": [
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"linesToDraw": [
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"p1x": "0",
"p1y": "0",
"p2x": "4",
"p2y": "0",
"attributes": {
"color": "GRAY",
"lineType": "BOLD",
"labels": [
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"p1x": "0",
"p1y": "0",
"p2x": "0",
"p2y": "2",
"attributes": {
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"labels": [
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"localBoundingBox": {
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Solution
Solution
Solution steps
Rewrite in the form of the standard ellipse equation
Therefore ellipse properties are:
therefore is semi-major axis and is semi-minor axis
Graph
Popular Examples
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Frequently Asked Questions (FAQ)
What is (x^2}{16}+\frac{y^2)/4 =1 ?
The solution to (x^2}{16}+\frac{y^2)/4 =1 is Ellipse with (h,k)=(0,0),a=4,b=2