Question

I need help for my assignment I need to submit today

Answer 1

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`