Question

Question #235c3

Answer 1

`(x+2)^2+(y-4)^2=6^2`

Hence, the Centre of the Circle is `(-2,4)` and Radius `=6.`

Explanation:

`x^2+y^2+4x-8y=16`

Completing the squares for the terms `x^2+4x` and `y^2-8y`, we

get

`(x^2+4x+4)+(y^2-8y+16)=16+4+16=36`

`:. (x+2)^2+(y-4)^2=6^2`

Hence, the Centre of the Circle is `(-2,4)` and Radius `=6.`

Answer 2

`(x+2)^2+(y-4)^2=36`

Explanation:

The standard form of the `color(blue)"equation of a circle"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))`
where (a ,b) are the coordinates of the centre and r, the radius.

`"Rearrange " x^2+y^2+4x-8y=16" into this form"`

`"Using the method of "color(blue)"completing the square"`

`rArrx^2+4x+y^2-8y=16`

`rArr(x^2+4xcolor(red)(+4))+(y^2-8ycolor(magenta)(+16))=16color(red)(+4)color(magenta)(+16)`

`rArr(x+2)^2+(y-4)^2=36larr" in standard form"`

`rArr"centre "=(-2,4)" and radius" =6`

`"These allow a sketch of the circle to be made"`
graph{(y^2-8y+x^2+4x-16)=0 [-25.31, 25.32, -12.66, 12.65]}