Answer:
[tex]x^2+y^2+4x-10y+20=0[/tex]
Step-by-step explanation:
Equation of a Circle
A circle in the plane is completely defined by two parameters: center and radius. If we know the center is at the point (h,k) and the radius is r, then the equation of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
However, that is not the standard form of an equation, we must ensure the equation is written as
[tex]Ax^2+By^2+Cx+Dy+E=0[/tex]
First, let's find the equation by replacing the known parameters of the circle:
[tex](x+2)^2+(y-5)^2=3^2=9[/tex]
To find the standard form, we only need to expand the indicated operations and simplify:
[tex]x^2+4x+4+y^2-10y+25=9[/tex]
[tex]x^2+y^2+4x-10y+25+4-9=0[/tex]
Simplifying
[tex]\boxed{x^2+y^2+4x-10y+20=0}[/tex]
