Question

Write the equation of a hyperbola with vertices (-5, 0) and (5, 0) and co-vertices at (0, -6) and (0, 6).

Write the equation of a hyperbola with foci at (-1, 1) and (5, 1) and vertices at (0, 1) and (4, 1).

Write the equation of a hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and (1, -3).

Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5).

Answer 1

please i need help.

Answer 2

1.
Given hyperbola has a horizontal transverse axis.
Its standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of centre
For given hyperbola:
centre:(0,0)
length of horizontal transverse axis=10=2a
a=5
a^2=25
length of co-vertices or conjugate axis=12=2b
b=6
b^2=36
Equation:
x^2/25-y^2/36=1

Answer 3

4.
(y-k)^2/a^2-(x-h)^2/b^2=1
y-coordinate of centre: mid point between y-coordinates of foci and vertices=3
x-coordinate of centre=3
centre: (3,3)

length of vertical transverse axis=-1 to 5=6=2a
a=3
a^2=9

foci:
2c=-3 to 7=10
c=5
c^2=25
c^2=a^2+b^2
b^2=c^2-a^2=25-9=16
b=√16=4
Equation of given hyperbola:
(y-k)^2/a^2-(x-h)^2/b^2=1
(y-2)^2/9-(x-2)^2/16=1

Answer 4

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