A. Given the following information about the hyperbola, find both its standard and general form:
1. FOCI: (-4, 0) (4, 0); VERTICES: (-3, 0) (3, 0)
2. FOCI: (-3, -3) (-3, 13); VERTICES: (-3, 0) (-3, 10)
B. Given the standard form of the equation of hyperbola, find the following, then sketch the graph:
A. orientation
B. opening of branches
C. center
D. transverse axis
E. conjugate axis
F. distance of the foci
G. vertices
H. foci
I. co-vertices
J. asymptotes
1.(x+4)^2/9 − (y+3)^2/4 = 1
2.(y+2)^2/36 − (x−1)^2/49 = 1
C. Convert each general form to standard form of the equation of hyperbola: (10 points)
1. 9y^2 − 4x^2 − 18y + 24x − 63 = 0
2. 9x^2 - 4y^2 - 90x + 32y - 163 = 0
A. 1. Basic “horizontal” hyperbola:
Equation:
Foci:
Vertices:
The standard form of an equation of a hyperbola
The general form of an equation of a hyperbola
2. The center is and the vertices are
Equation:
Foci:
The standard form of an equation of a hyperbola
The general form of an equation of a hyperbola
B.
1.
A. Horizontal oriented hyperbola
B. Opens left and right.
C. Center
D. Major (transverse) axis length: 6
E. Minor (conjugate) axis length: 4
F.
Focal Parameter:
G. Vertices:
H. Foci:
I. Co-vertices:
J. Asymptotes:
2.
A. Verticaloriented hyperbola
B. Opens upward and downward.
C. Center
D. Major (transverse) axis length: 12
E. Minor (conjugate) axis length: 14
F.
Focal Parameter:
G. Vertices:
H. Foci:
I. Co-vertices:
J. Asymptotes:
C.
1.
2.
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