Answer:
The equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].
Step-by-step explanation:
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] .... (1)
where, (h,k) is the center of the circle and r is the radius.
It is given that the center of the circle is (-5,-8). it means h=-5 and k=-8.
The circle passes through the point (2,-8). So, the radius of the circle is the distance between point (-5,-8) and (2,-8).
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]r=\sqrt{(2-(-5))^2+(-8-(-8))^2}[/tex]
[tex]r=\sqrt{7^2+0}[/tex]
[tex]r=7[/tex]
Substitute h=-5, k=8 and r=7 in equation (1), to find the equation of circle.
[tex](x-(-5))^2+(y-(08))^2=(7)^2[/tex]
[tex](x+5)^2+(y+8)^2=49[/tex]
Therefore the equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].
