Question

Write the center and radius for the following circles

Answer 1

Given:

The equations of circle are

4.
`\left(x+(2)/(3)\right)^2+(y+1)^2=24`

5.
`(x-1)^2+(y+2)^2=28`

6 .
`(x+12)^2+y^2=(3)/(64)`

To find:

The center and radius for the given circles.

Solution:

The standard form of a circle is:

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

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

4.

The equation of the circle is

`\left(x+(2)/(3)\right)^2+(y+1)^2=24`

The standard form of this circle is

`\left(x-(-(2)/(3))\right)^2+(y-(-1))^2=(√(24))^2`

`\left(x-(-(2)/(3))\right)^2+(y-(-1))^2=(2√(6))^2`

Therefore, the center of the circle is
`\left(-(2)/(3),-1\right)` and the radius of the circle is
`2√(6)`.

5.

The equation of the circle is

`(x-1)^2+(y+2)^2=28`

The standard form of this circle is

`(x-1)^2+(y-(-2))^2=(√(28))^2`

`(x-1)^2+(y-(-2))^2=(2√(7))^2`

Therefore, the center of the circle is
`\left(1,-2\right)` and the radius of the circle is
`2√(7)`.

6.

The equation of the circle is

`(x+12)^2+y^2=(3)/(64)`

The standard form of this circle is

`(x-(-12))^2+(y-0)^2=(\sqrt{(3)/(64)})^2`

`(x-(-12))^2+(y-0)^2=(√(3))/(8)`

Therefore, the center of the circle is
`\left(-12,0\right)` and the radius of the circle is
`(√(3))/(8)`.