SOLUTION: Find an equation of the hyperbola Center at the origin, its foci on the y axis and passing through the points (-2,4) and (-6,7)

Question 792750: Find an equation of the hyperbola Center at the origin, its foci on the y axis and passing through the points (-2,4) and (-6,7)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find an equation of the hyperbola Center at the origin, its foci on the y axis and passing through the points (-2,4) and (-6,7)
***
Given foci data shows that hyperbola has a vertical transverse axis.
Its standard form of equation with center at the origin:
..
Using coordinates of 2 given points(-2,4) and (-6,7)
Form two equations:
16/a^2-4/b^2=1
49/a^2-36/b^2=1
subtract
-33/a^2+32/b^2=0
33/a^2=32/b^2
a^2=(33/32)b^2
..
16/a^2-4/b^2=1
16/(33/32)b^2-4/b^2=1
LCD:(33/32)b^2
16-33/8=(33/32)b^2
128/8-33/8=(33/32)b^2
95/8=(33/32)b^2
b^2=380/33
a^2=(33/32)(380/33)=380/32
Equation:

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