Given:
The center of the circle = (-1,0)
Point on the circle = (2,-4).
To find:
The equation of the circle.
Solution:
Distance between two points is
Distance between the center (-1,0) and the point on the circle (2,-4) is the radius of the circle.
On further simplification, we get
Now, the equation of the circle is
Where, (h,k) is the center and r is the radius of the circle.
The radius of the circle is 5 and the center is at (-1,0), so the equation of the circle is
Therefore, the first option is correct, i.e., .