Answer:
For the given equation of circle, radius of circle 3√3 units.
Step-by-step explanation:
Here, the given equation of the circle is[tex]x^{2} + y^{2} + 4x - 24 = -1[/tex]
Now, the equation o f circle is given as [tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Here, (h,k) = Center coordinates
r = Radius of the circle
Now, convert the given equation in the required form:
[tex]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[/tex]
⇒[tex](x+2)^2 + y^2 = 27[/tex]
or,comparing it with the circle equation:
we see [tex](x -(-2))^2 + (y-0)^2 = (3\sqrt{3} )^2[/tex]
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.
