Question #235c3

2 Answers
Ratnaker Mehta
Apr 6, 2017

(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.

Jim G.
Apr 6, 2017

(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]}

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