Write the standard form of the equation of the circle shown.

The stand form of the circle is

here (h,k) is the center of the cirlce and (x,y) is the point on the circle.

In our case (h,k) is (-2,2)

so our circle equation is

.      ----------- (i)

and we can find our r by finding the distance between center and the point given on the circle. lets say we take (1,0) point given on the circle according to our diagram

Then

so by putting the values of r in equation (i)

Which is our third option.

Step-by-step explanation:

We are given a circle with a center at the point (4, -5) and two points on the circle (-5, 0) and (1, 0).

We know that the standard form of equation of a circle is:

So putting the given values to get the value of radius (r):

Substituting the value of radius to get the equation of the circle:

Taking square on both the sides:

Therefore, the equation of the given circle is .

the solution is 12x-6y