Answer:
[tex](x+3)^2+(y+11)^2=121[/tex]
Step-by-step explanation:
Consider a sketch of the problem as shown in the picture, where:
- Blue line is given by y = 4x + 1.
- Point B is the center of the circle.
- Point A is (-3, 0).
Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.
So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.
Since the general equation of the circle of radius lenght r centered at (h, k) is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
then with h = -3, k = -11 and r= 11, the equation of our circle is
[tex](x+3)^2+(y+11)^2=121[/tex]
