Finding the Standard Equation of a Hyperbola In Exercises 41–48, find the standard form of the equation of the hyperbola with the given characteristics. Vertices: ( 2, ±3 ) Point on graph: ( 0 , 5 )
Finding the Standard Equation of a Hyperbola In Exercises 41–48, find the standard form of the equation of the hyperbola with the given characteristics. Vertices: ( 2, ±3 ) Point on graph: ( 0 , 5 )
Solution Summary: The author explains the standard equation of hyperbola with the characteristics vertex at (2,pm 3) and point on the graph is
Finding the Standard Equation of a Hyperbola In Exercises 41–48, find the standard form of the equation of the hyperbola with the given characteristics.
In Exercises 5–12, find the standard form of the equation of each
hyperbola satisfying the given conditions.
5. Foci: (0, –3), (0, 3); vertices: (0, –1), (0, 1)
6. Foci: (0, –6), (0, 6); vertices: (0, -2), (0, 2)
7. Foci: (-4, 0), (4, 0); vertices: (-3, 0), (3,0)
8. Foci: (-7, 0), (7, 0); vertices: (-5, 0), (5,0)
9. Endpoints of transverse axis: (0, -6), (0, 6); asymptote:
y = 2x
10. Endpoints of transverse axis: (-4,0), (4, 0); asymptote:
y = 2r
11. Center: (4, -2); Focus: (7, -2); vertex: (6, -2)
12. Center: (-2, 1); Focus: (-2, 6); vertex: (-2, 4)
In Exercises 3–10, describe the curve represented by each equation.
Identify the type of curve and its center (or vertex if it is a parabola).
Sketch each curve.
Exercises 27–34 give equations for hyperbolas. Put each equation instandard form and find the hyperbola’s asymptotes. Then sketch thehyperbola. Include the asymptotes and foci in your sketch.27. x2 - y2 = 1
28. 9x2 - 16y2 = 14429. y2 - x2 = 8
30. y2 - x2 = 431. 8x2 - 2y2 = 16
32. y2 - 3x2 = 333. 8y2 - 2x2 = 16
34. 64x2 - 36y2 = 2304
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