We have a circle with a center of (-2, 7) and a radius of 13.......the equation is
(x + 2)^2 + (y - 7)^2 = 13^2
Manipulating the equation of the line we have that x = 2y + 10
Sub this into the circle equation
(2y + 10 + 2)^2 + ( y - 7)^2 = 13^2
(2y + 12)^2 + ( y - 7)^2 = 169
4y^2 + 48y + 144 + y^2 - 14y + 49 = 169
5y^2 + 34y + 24 = 0 factor
(5y + 4) ( y + 6) = 0
Set each factor to 0 and solve for y
5y + 4 = 0 y + 6 = 0
5y = - 4 y = - 6
y = - 4/5
And
x = 2 (-4/5) + 10 x = 2(-6) + 10
x = -8/5 + 50/5 x = -2
x = 42/5
The intersection points are (-2, - 6) and (42/5, -4/5)