+128475 In the equation of the circle.....sub 2x + 11 for y......and we have
( x + 5)^2 + ( 2x + 11 - 6)^2 = 25 simplify
x^2 + 10x + 25 + ( 2x + 5)^2 = 25
x^2 + 10x + 25 + 4x^2 + 20x + 25 = 25
5x^2 + 30x + 50 = 25 subtract 25 from both sides
5x^2 + 30 x + 25 = 0 factor out 5
5 ( x^2 + 6x + 5) = 0 divide both sides by 5
x^2 + 6x + 5 = 0
Factor x^2 + 6x + 5 = 0 as
(x + 5) ( x + 1) = 0
Set each factor to 0 and solve for x and we have
x = - 5 and x = - 1
These are the x coordinates of the intersections...and the y coordinates are
y = 2(-5) + 11 = 1 and y = 2(-1) + 11 = 9
So...the intersection points are
(-5, 1) and ( -1, 9)
