exam Maths Puzzle Numerical Ability

I can go back and graph what i see out of problems but not write the equation correctly. how do i write an equation for a hyperbola in standard form with vertices (0,8) (0,-8) and asymptotes y=positive or negative 4x?

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7c(8c+7)=3c-15
what is the name of the equation: am = a1 + (m-1)d and its companion: Sm = (m/2) (2a+(m-1)d)

this equation is related to the 1+2+3+4+5...100 problem that a young German student