Solution 4.1:6a

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If we write the equation as


\displaystyle \left( x-0 \right)^{2}+\left( y-0 \right)^{2}=9


we can interpret the left-hand side as the square of the distance between the points \displaystyle \left( x \right.,\left. y \right) and \displaystyle \left( 0 \right.,\left. 0 \right). The whole equation says that the distance from a point ( \displaystyle \left( x \right.,\left. y \right) to the origin should be constant and equal to \displaystyle \sqrt{9}=3, which describes a circle with its centre at the origin and radius \displaystyle \text{3}.