Answer:
Option C
Step-by-step explanation:
The standard form of equation of circle is:
(x-h)^2+ (y-k)^2=r^2
As we only know two points on the circle which are the ends of diameter.
As we know
Radius=Diameter/2
We have to find the length of diameter using the distance formula first to calculate radius. So,
Diameter= √((-11-(+5))^2+(-3-(-3)^2 )
= √((-11+5)^2+(-3+3)^2 )
=√((-6)^2+(0)^2 )
= √36
=6
Now,
Radius=6/2
=3
As the diameter passes through centre, so the mid-point of diameter will be centre of the circle:
Mid-point=((x_1+x_2)/2,(y_1+y_2)/2)
=((-5-11)/2,(-3-3)/2)
=((-16)/2,(-6)/2)
=(-8,-3)
Putting the values of radius and centre in standard form
(x-h)^2+ (y-k)^2=r^2
(x-(-8))^2+ (y-(-3))^2=3^2
(x+8)^2+ (y+3)^2=9
So the correct answer is option C ..