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Find an equation of the hyperbola having foci at (-1,1-sqrt52), and -1,1+sqrt52) and asymptotes at y=2/3x+5/3 and y=-2/3x+1/3
I know c = sqrt of 52 and c^2 = 52 I am just unsure on how to find A and B. I know how to graph the asymptotes and I know the center is (-1,1)
I know I have to use 2/3 for A and B I just dont understand how.
From given Foci coordinates you can see that this is a hyperbola with vertical transverse axis.
(y changes but x does not)
Standard form for hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being (x,y) coordinates of center
Slope, m, for asymptotes of this form=a/b
From given asymptote equations, m=±2/3
see graph below as a visual check on the answer