Question

determine as coordenadas do foco da hiperbole de equação
$\frac{ {(x - 1)}^{2} }{7} - \: \frac{ {(y - 2)}^{2} }{2} = 1$
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Answer 1

${a}^{2}=2\\{b}^{2}=7\\{c}^{2}={a}^{2}+{b}^{2}\\{c}^{2}=7+2=9\rightarrow\,c=\sqrt{9}=3$

$-b=-2\\b=2$

$-a=-1\times(-1)\\a=1$

$F_{1}(a-c,y_{0})\\F_{2}(a+c,y_{0})$

$\boxed{\boxed{\mathsf{F_{1}(-2,2)\:F_{2}(4,2)}}}$