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The equation of a hyperbola in the form , where b = 10. The lower arm of the hyperbola would represent the arch.

((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=-1

i have 2 questions about this number one shouldn't the equations be

((x-h)^2)/(b^2)-((y-k)^2)/(a^2)=-1 because it should be a hyberbola that opens up and down?

and second how do i solve this?