Question

What is the equation of the circle with a center at `(4 ,-1 )` and a radius of `8`?

Answer 1

`x^2+y^2-8x+2y-47=0`

Explanation:

the eqn of a circle centre `(a,b)` and radius `r`

`(x-a)^2+(y-b)^2=r^2`

#we ahve

`(x-4)^2+(y- -1)^2=8^2`

`(x-4)^2+(y+1)^2=64`

`x^2-8x+16+y^2+2y+1=64`

`x^2+y^2-8x+2y-47=0`

Answer 2

`(x-4)^2+(y+1)^2=64`

Explanation:

`"the equation of a circle in standard form 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"`

`"here "(a,b)=(4,-1)" and "r=8`

`(x-4)^2+(y-(-1))^2=8^2`

`(x-4)^2+(y+1)^2=64larrcolor(red)"equation of circle"`