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Question Number 122319 by help last updated on 15/Nov/20

Commented by help last updated on 15/Nov/20

$$explainyouranswerpls$$

Answered by 676597498 last updated on 15/Nov/20

$${(x-\frac{3}{2})}^2-{(y+2)}^2=\frac{13}{4}$$$$\frac{{(x-\frac{3}{2})}^2}{{\left(\frac{\sqrt{13}}{2}\right)}^2}-\frac{{(y+2)}^2}{{\left(\frac{\sqrt{13}}{2}\right)}^2}=1$$

Answered by MJS_new last updated on 15/Nov/20

$$x^2-3x-y^2+4y=5$$$$x^2-3x+\frac{9}{4}-y^2+4x-4=5+\frac{9}{4}-4$$$${(x-\frac{3}{2})}^2-{(y-2)}^2=\frac{13}{4}$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{hyperbola}\mathrm{with}\mathrm{center}\left(\begin{array}{c}3/2\\ 2\end{array}\right)$$$$\mathrm{and}a=b=\frac{\sqrt{13}}{2}\mathrm{and}e=\frac{\sqrt{26}}{2}\mathrm{and}ϵ=\sqrt{2}$$

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