# Chapter 13 - Conic Sections - 13.1 Conic Sections: Parabolas and Circles - 13.1 Exercise Set - Page 854: 8

part $\left( e \right)$

#### Work Step by Step

The standard form of the equation of the circle centred at $\left( h,k \right)$ with the radius r is defined as, ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ Compare the provided equation with the standard form of the equation of the circle. It shows that the provided equation is the equation of a circle. The values of $h\text{ and }k$ are obtained as: \begin{align} & x-h=x+2 \\ & -h=2 \\ & h=-2 \end{align} And, \begin{align} & y-k=y-5 \\ & -k=-5 \\ & k=5 \end{align} So, the centre of the circle is obtained as $\left( -2,5 \right)$. Therefore, the correct match for the graph of the equation ${{\left( x+2 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=9$ is part (e).

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