Q:

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

Accepted Solution

A:
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 circleNow, 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.