Question

How do you write an equation of a circle with center at (0,5), d=20?

Answer 1

Assuming `d` is the radius, the answer is `x^2 + (y-5)^2 = 20^2`

Explanation:

I'm not sure what `d` is here, let's assume it's the radius.

The general equation of a circle with center `(a,b)` and radius `r` is

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

So in our case that's

`(x - 0)^2 + (y - 5)^2 = 20^2`

`x^2 + (y-5)^2 = 400`

Answer 2

`x^2+(y-5)^2=100`

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"`

`"here "(a,b)=(0,5)" and r=d/2=20/2=10`

`rArr(x-0)^2+(y-5)^2=10^2`

`rArrx^2+(y-5)^2=100larrcolor(red)"equation of circle"`