{
"query": {
"display": "vertices $$\\frac{x^{2}}{25}-\\frac{y^{2}}{9}=1$$",
"symbolab_question": "CONIC#vertices \\frac{x^{2}}{25}-\\frac{y^{2}}{9}=1"
},
"solution": {
"level": "PERFORMED",
"subject": "Geometry",
"topic": "Hyperbola",
"subTopic": "vertices",
"default": "(5,0),(-5,0)",
"meta": {
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}
},
"steps": {
"type": "interim",
"title": "Hyperbola vertices given $$\\frac{x^{2}}{25}-\\frac{y^{2}}{9}=1:{\\quad}\\left(5,\\:0\\right),\\:\\left(-5,\\:0\\right)$$",
"steps": [
{
"type": "definition",
"title": "Hyperbola vertices",
"text": "The vertices $$\\left(h+a,\\:k\\right),\\:\\left(h-a,\\:k\\right)\\:$$are the two bending points of the hyperbola with center $$\\left(h,\\:k\\right)\\:$$and semi-axis $$a,\\:b.\\:$$"
},
{
"type": "step",
"result": "\\left(h+a,\\:k\\right),\\:\\left(h-a,\\:k\\right)"
},
{
"type": "step",
"primary": "Calculate Hyperbola properties"
},
{
"type": "interim",
"title": "$$\\frac{x^{2}}{25}-\\frac{y^{2}}{9}=1:\\quad$$Right-left Hyperbola with $$\\left(h,\\:k\\right)=\\left(0,\\:0\\right),\\:a=5,\\:b=3$$",
"input": "\\frac{x^{2}}{25}-\\frac{y^{2}}{9}=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 $$\\frac{x^{2}}{25}-\\frac{y^{2}}{9}=1\\:$$in the form of a standard hyperbola equation",
"result": "\\frac{\\left(x-0\\right)^{2}}{5^{2}}-\\frac{\\left(y-0\\right)^{2}}{3^{2}}=1"
},
{
"type": "step",
"primary": "Therefore Hyperbola properties are:",
"result": "\\left(h,\\:k\\right)=\\left(0,\\:0\\right),\\:a=5,\\:b=3"
}
],
"meta": {
"interimType": "Hyperbola RightLeft Top Title 3Eq"
}
},
{
"type": "step",
"result": "\\left(0+5,\\:0\\right),\\:\\left(0-5,\\:0\\right)"
},
{
"type": "step",
"primary": "Refine",
"result": "\\left(5,\\:0\\right),\\:\\left(-5,\\:0\\right)"
}
],
"meta": {
"solvingClass": "Hyperbola"
}
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Solution
vertices
Solution
Solution steps
Calculate Hyperbola properties
Right-left Hyperbola with
Refine
Graph
Popular Examples
Frequently Asked Questions (FAQ)
What is the vertices (x^2}{25}-\frac{y^2)/9 =1 ?
The vertices (x^2}{25}-\frac{y^2)/9 =1 is (5,0),(-5,0)