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Question 563654: This hyperbola is centered at (21, -14), and the length of its transverse axis is 24. Which of the equations below could be its equation?
A. (y-14)^2/15^2-(x+21)^2/12^2=1
b. (x-21)^2/15^2-(y+14)^2/12^2=1
c. (x-21)^2/12^2-(y-14)^2/15^2=1
d. (x-21)^2/12^2-(y+14)^2/15^2=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! This hyperbola is centered at (21, -14), and the length of its transverse axis is 24. Which of the equations below could be its equation?
A. (y-14)^2/15^2-(x+21)^2/12^2=1
b. (x-21)^2/15^2-(y+14)^2/12^2=1
c. (x-21)^2/12^2-(y-14)^2/15^2=1
d. (x-21)^2/12^2-(y+14)^2/15^2=1
**
Standard form of equation for hyperbola with horizontal transverse axis:
(x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
For given hyperbola:
center: (21,-14)
Transverse axis=24=2a
a=12
a^2=12^2
..
By process of elimination:
A) does not have correct center coordinates
b) has a^2=12^2 listed under the y-term which means the transverse axis is vertical and the y-term should be listed first before the x-term, but it is not.
c) also does not have correct center coordinates
d) it has the correct center coordinates and a^2=12^2 is listed under the x-term which means the transverse axis is horizontal and the x-term should be listed first as it is. So, this is the best answer.
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