{
"query": {
"display": "axis $$\\frac{x^{2}}{9}-\\frac{y^{2}}{4}=1$$",
"symbolab_question": "CONIC#axis \\frac{x^{2}}{9}-\\frac{y^{2}}{4}=1"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Hyperbola",
"subTopic": "axis",
"default": "a=3,b=2"
},
"steps": {
"type": "interim",
"title": "Hyperbola Axis given $$\\frac{x^{2}}{9}-\\frac{y^{2}}{4}=1:{\\quad}a=3,\\:b=2$$",
"input": "\\frac{x^{2}}{9}-\\frac{y^{2}}{4}=1",
"steps": [
{
"type": "definition",
"title": "Hyperbola standard equation",
"text": "$$\\frac{\\left(x-h\\right)^{2}}{a^2}-\\frac{\\left(y-k\\right)^{2}}{b^2}=1\\:$$ is the standard equation for a right-left facing hyperbola<br/>with center $$\\bold{\\left(h,\\:k\\right)},\\:$$ semi-axis $$\\bold{a}$$ and semi-conjugate-axis $$\\bold{b}$$."
},
{
"type": "step",
"primary": "Rewrite $$\\frac{x^{2}}{9}-\\frac{y^{2}}{4}=1\\:$$in the form of a standard hyperbola equation",
"result": "\\frac{\\left(x-0\\right)^{2}}{3^{2}}-\\frac{\\left(y-0\\right)^{2}}{2^{2}}=1"
},
{
"type": "step",
"primary": "Therefore Hyperbola properties are:",
"result": "\\left(h,\\:k\\right)=\\left(0,\\:0\\right),\\:a=3,\\:b=2"
},
{
"type": "step",
"primary": "And the axes are:",
"result": "a=3,\\:b=2"
}
],
"meta": {
"solvingClass": "Hyperbola"
}
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Solution
axis
Solution
Solution steps
Rewrite in the form of a standard hyperbola equation
Therefore Hyperbola properties are:
And the axes are:
Graph
Popular Examples
Frequently Asked Questions (FAQ)
What is the axis (x^2)/9-(y^2)/4 =1 ?
The axis (x^2)/9-(y^2)/4 =1 is a=3,b=2