A hyperbola has equation ${{y}^{2}}+2dy-{{x}^{2}}+2x=2-{{d}^{2}}$, where $d$ is a real constant. Sho

Question

A hyperbola has equation ${{y}^{2}}+2dy-{{x}^{2}}+2x=2-{{d}^{2}}$, where $d$ is a real constant. Show that the equation of the hyperbola can be expressed as ${{\left( y+d \right)}^{2}}-{{\left( x-1 \right)}^{2}}=1$. [2] It is given that one of the asymptotes for the hyperbola has equation $y=x-8$. Find the value of $d$ and hence write down the equation of the other asymptote. [5]

Accepted Answer

(i) $(y+d)^2-(x-1)^2=1$; (ii) $d=7$, other asymptote $y=-x-6$

2022 TMJC J1 MYE Q2

2022 TMJC J1 MYE Q2

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