Question 741932
Find an equation for the hyperbola describes.
Center at (2,1); focus at (-5,1); vertex at (1,1)
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Hyperbola as described has a horizontal transverse axis. (x-coordinates change but y-coordinates do not.)
Its standard form of equation: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
For given hyperbola:
center: (2,1) (given)
a=1(distance from center to vertex on the horizontal transverse axis)(2 to 1)
a^2=1
c=7(distance from center to focus on the horizontal transverse axis)(2 to -5)
c^2=49
c^2=a^2+b^2
b^2=c^2-a^2=49-1=48
Equation of given hyperbola:
 {{{(x-2)^2-(y-1)^2/48=1}}}