4.)
Standard equation of a circle:
[tex]({x - h})^{2} + ({y - k})^{2} = {r}^{2} [/tex]
Given center at ( h, k ) which is equal to ( - 4, - 2), we can partially write the equation as:
[tex]({x + 4 })^{2} + ({y + 2})^{2} = {r}^{2} [/tex]
Since P(2,1) is a point which is part of the solution of the circle, we can simply substitute it to the equation of the circle in order to find r.
Let
[tex] {(2 + 4)}^{2} + {(1+ 2)}^{2} = {r}^{2} \\ 36 + 9 = {r}^{2} \\ 45 = {r}^{2} [/tex]
Therefore, the equation of the circle in standard form:
[tex] {(x + 4)}^{2} + {(y + 2)}^{2} = 45[/tex]
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4.)
Standard equation of a circle:
[tex]({x - h})^{2} + ({y - k})^{2} = {r}^{2} [/tex]
Given center at ( h, k ) which is equal to ( - 4, - 2), we can partially write the equation as:
[tex]({x + 4 })^{2} + ({y + 2})^{2} = {r}^{2} [/tex]
Finding r:
Since P(2,1) is a point which is part of the solution of the circle, we can simply substitute it to the equation of the circle in order to find r.
Let
[tex] {(2 + 4)}^{2} + {(1+ 2)}^{2} = {r}^{2} \\ 36 + 9 = {r}^{2} \\ 45 = {r}^{2} [/tex]
Therefore, the equation of the circle in standard form:
[tex] {(x + 4)}^{2} + {(y + 2)}^{2} = 45[/tex]