Question

How do you write an equation for a circle with center (-8, 13) and radius 8?

Answer 1

`(x+8)^2 +(y -13)^2 = 64`

Explanation:

The standard form of the equation of a circle is.

`color(red)(|bar(ul(color(white)(a/a)color(black)( (x-a)^2 + (y-b)^2 = r^2)color(white)(a/a)|)))`
where (a ,b) are the coords of the centre and r,the radius

here a = -8 , b = 13 and r = 8

`rArr (x + 8)^2 + (y - 13)^2 = 64" is the equation"`

Expanding the brackets, rearranging the terms and equating to zero gives another form of the equation.

`color(red)(|bar(ul(color(white)(a/a)color(black)( x^2 +y^2 + 2gx + 2fy + c = 0 )color(white)(a/a)|)))`

`rArr (x+8)^2 +(y-13)^2 = 64 " becomes "`

`x^2 + 16x + 64 + y^2 - 26y + 169 - 64 = 0`

`rArr x^2 + y^2 + 16x - 26y + 169 = 0" is another form "`