Question

x2+y2+4x-24=-1 The equation of a circle in the cycle-plane is the shown above. what is the radius of the circle

Answer 1

For the given equation of circle, radius of circle 3√3 units.

Explanation:

Here, the given equation of the circle is
`x^(2)  + y^(2)  + 4x    - 24  = -1`

Now, the equation o f circle is given as
`(x-h)^2 + (y-k)^2  = r^2`

Here, (h,k) = Center coordinates

r = Radius of the circle

Now, convert the given equation in the required form:

`x^(2)  + y^(2)  + 4x    - 24  = -1  \implies  x^(2)  + y^(2)  + 4x    - 24 + (2)^2  - (2)^2 = -1  \\or,  x^(2) + 4x +(2)^2 + y^2 - 24 - 4 = -1\\\implies(x+2)^2 + y^2 = -1 + 28\\or, (x+2)^2 + y^2  = 27`

⇒
`(x+2)^2 + y^2  = 27`

or,comparing it with the circle equation:

we see
`(x -(-2))^2 + (y-0)^2 = (3√(3) )^2`

So, it implies here, (h,k) = (-2, 0) and radius r = 3√3 units.

Hence, for the given equation of circle, radius of circle 3√3 units.