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I need help for my assignment I need to submit today-example-1

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The general equation of a circle is expressed as


\begin{gathered} (x-a)^2+(y-b)^2=r^2\text{ ----- equation 1} \\ \text{where} \\ (a,\text{ b)}\Rightarrow\text{ center of the circle} \\ r\Rightarrow radius\text{ of the circle} \end{gathered}

Given that a circle having equation


\begin{gathered} (x-2)^2+(y-5)^2\text{ = 16} \\ \Rightarrow(x-2)^2+(y-5)^2\text{ = }4^2 \end{gathered}

is moved up 3 units and 1 unit to the left. Thus, we have


\begin{gathered} (x-2+1)^2+(y-5-3)^2\text{ = }4^2 \\ \end{gathered}

This gives


(x-1)^2+(y-8)^2\text{ = }4^2\text{ ----- equation 2}

Comparing equations 1 and 2, we have


a\text{ = 1, b = 8, r = 4}

Hence,

the center (a, b) of the circle is (1, 8),

the radius r of the circle is 4,

the equation of the circle is


(x-1)^2+(y-8)^2=4^2

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