In the xy-plane, the graph of #2x^2-6x+2y^2+2y=45# is a circle? What is the radius of the circle?

1 Answer
Mar 24, 2017

Answer:

#"radius " =5#

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.

The first step is to divide all terms by 2

#rArrx^2-3x+y^2+y=45/2#

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

#x^2-3xcolor(red)(+9/4)+y^2+ycolor(red)(+1/4)=45/2color(red)(+9/4+1/4)#

#rArr(x-3/2)^2+(y+1/2)^2=25larrcolor(blue)" standard form"#

#r^2=25rArrr=5#