Describe the hyperbola y2−(x−1)24=1y^2-\frac{\left(x-1\right)^2}{4}=1.

This is a vertical hyperbola centered at ( 1 , 0 ) \left(1,0\right) with vertices at ( 1 , 1 ) , ( 1 , − 1 ) \left(1,1\right),\left(1,-1\right) and foci at ( 1 , 5 ) , ( 1 , − 5 ) \left(1,\sqrt5\right),\left(1,-\sqrt5\right) .

Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations1h 31m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

8. Conic Sections

Hyperbolas NOT at the Origin

College Algebra8. Conic SectionsHyperbolas NOT at the Origin

Multiple Choice

Describe the hyperbola $y^{2} - \frac{{(x - 1)}^{2}}{4} = 1$ .

This is a vertical hyperbola centered at $open paren 1 comma 0 close paren$ with vertices at $open paren 1 comma 1 close paren comma open paren 1 comma negative 1 close paren$ and foci at $(1, \sqrt{5}), (1, - \sqrt{5})$ .

This is a vertical hyperbola centered at $open paren 1 comma 0 close paren$ with vertices at $open paren 1 comma 2 close paren comma open paren 1 comma negative 2 close paren$ and foci at $open paren 1 comma 1 close paren comma open paren 1 comma negative 1 close paren$ .

This is a horizontal hyperbola centered at $open paren negative 1 comma 0 close paren$ with vertices at $open paren 0 comma 0 close paren comma open paren negative 2 comma 0 close paren$ and foci at $(\sqrt{5} - 1, 0), (- \sqrt{5} - 1, 0)$ .

This is a horizontal hyperbola centered at $open paren 1 comma 0 close paren$ with vertices at $open paren 0 comma 0 close paren comma open paren negative 2 comma 0 close paren$ and foci at $(1, \sqrt{5}), (1, - \sqrt{5})$ .

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Describe the hyperbola $y^{2} - \frac{{(x - 1)}^{2}}{4} = 1$ .