Answer:
The equation of the given circle in general form is given by:
Option: A
[tex]x^2+y^2+4x+2y-44=0[/tex]
Step-by-step explanation:
We know that the general equation of a circle with center at (h,k) and radius 'r' is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Clearly from the figure we have:
The center of the circle is at (-2,-1) and radius is 7 units.
i.e. we have: (h,k)=(-2,-1) and r=7
Hence, the equation of the circle is given by:
[tex](x-(-2))^2+(y-(-1))^2=7^2\\\\\\(x+2)^2+(y+1)^2=49[/tex]
on expanding the terms we have:
[tex]x^2+4+4x+y^2+1+2y=49\\\\\\x^2+y^2+4x+2y+5-49=0\\\\\\x^2+y^2+4x+2y-44=0[/tex]
Hence, the general equation of the circle is:
[tex]x^2+y^2+4x+2y-44=0[/tex]
