+613 Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$
+1952 If we drew the graph for all the points 5 units away from (2, 7), we would get a circle with radius √5 and center (2, 7).
A circle like that would have the equation (x−2)2+(y−7)2=25.
Now, we just have to find the intersection points with the graph of y=5x−28.
We get a system of equations like this, and we just have to find (x, y). Luckily, y is already isolated in the second equation, so we just have to sub that into the first equation. We get
(x−2)2+(5x−28−7)2=25(x−2)2+(5x−35)2=25
x2−4x+4+25x2−350x+1225=2526x2−354x+1204=0
From this, we getx=86/13,7
Plugging these back for y, we get y=66/13,7.
This means our two points are (86/13, 66/13) & (7, 7)
Thanks! :)
