Question

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

Answer 1

`"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`