Question

Question #3894b

Answer 1

`(x+2)^2+(y+1)^2=13`

Explanation:

`"the standard form of the 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"`
`"is the radius"`

`"the centre is given and the distance from the centre to a "`
`"point on the circumference is the radius"`

`"to calculate r use the "color(blue)"distance formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(r=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(-2,-1)" and "(x_2,y_2)=(-5,-3)`

`r=sqrt((-5+2)^2+(-3+1)^2)=sqrt(9+4)=sqrt13`

`rArr(x-(-2))^2+(y-(-1))^2=(sqrt13)^2`

`rArr(x+2)^2+(y+1)^2=13" is the equation"`
graph{(x+2)^2+(y+1)^2-13=0 [-10, 10, -5, 5]}