Step-by-step explanation:
[tex]x^2+(y-k)^2=36[/tex]
[tex]y=5x+k[/tex]
Substituting y in the first equation
[tex]x^2+(5x+k-k)^2=36\\\Rightarrow x^2+25x^2=36\\\Rightarrow 26x^2=36\\\Rightarrow x^2=\frac{36}{26}\\\Rightarrow x=\sqrt{\frac{36}{26}}\\\Rightarrow x=\pm 1.17[/tex]
At x = 1.17
[tex]y=5\times 1.17+k\\\Rightarrow y=5.85+k[/tex]
At x = -1.17
[tex]y=5\times -1.17+k\\\Rightarrow y=-5.85+k[/tex]
The intersection points are (1.17, 5.85k) and (-1.17, -5.85k)
The graph would intersect regardless of what value k is.
