Question

How do you write an equation for a circle given center (-8,7) and radius is 1/2 units?

Answer 1

`(x+8)^2+(y-7)^2=1/4`

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 the radius"`

`"here " (a,b)=(-8,7)" and " r=1/2`

`rArr(x-(-8))^2+(y-7)^2=(1/2)^2`

`rArr(x+8)^2+(y-7)^2=1/4" is the equation"`

Answer 2

`(x+8)^2 + (y-7)^2 = 1/4`

Explanation:

The standard form for an equation of a circle is given by

`(x-h)^2 + (y-k)^2 = r^2`

where

• `h` is the `x`-coordinate for the center of the circle

• `k` is the `y`-coordinate for the center of the circle

• `r` is the radius of the circle

Plugging In known values, we have

`(x-(-8))^2 + (y-(7))^2 = (1/2)^2`

`color(red)((x+8)^2 + (y-7)^2 = 1/4`