Question

Write an equation for a circle with center at (–8, –9) and diameter 6.

Answer 1

The equation of circle is
`(x+8)^2+(y+9)^2=9`.

Explanation:

It is given that the diameter of circle is 6 units and the center of circle is (-8,-9).

The standard form of a circle is

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

Where, (h,k) is center of the circle and r is radius.

The diameter of circle is twice of its radius

`d=2r`

`6=2r`

`r=3`

The radius of the circle is 3 and the center of circle is (-8,-9). So, the required equation of circle is

`(x-(-8))^2+(y-(-9))^2=3^2`

`(x+8)^2+(y+9)^2=9`

Therefore the equation of circle is
`(x+8)^2+(y+9)^2=9`.