Answer:
The equation of the circle is [tex](x + 1)^2 + y^2 = 25[/tex]
Step-by-step explanation:
Equation of a circle:
The equation of a circle of centre [tex](x_c,y_c)[/tex] has the following format:
[tex](x - x_c)^2 + (y - y_c)^2 = r^2[/tex]
In which r is the radius.
Center (-1,0)
This means that [tex]x_c = -1, y_c = 0[/tex]. So
[tex](x - x_c)^2 + (y - y_c)^2 = r^2[/tex]
[tex](x - (-1))^2 + (y - 0)^2 = r^2[/tex]
[tex](x + 1)^2 + y^2 = r^2[/tex]
Finding the radius:
Distance between the radius and the centre and a point of the circle. In this case, point (2,-4). Using the formula for the distance between two points:
[tex]r = \sqrt{(2-(-1))^2+(-4-0)^2} = \sqrt{3^2 + 4^2} = \sqrt{25} = 5[/tex]
So, the equation of the circle is:
[tex](x + 1)^2 + y^2 = 5^2[/tex]
[tex](x + 1)^2 + y^2 = 25[/tex]
