Find the point in the first quadrant where the line y = 4 x intersects a circle of radius 7 centered at the origin.

Answer 1

A circle with radius 7 centered at the origin is x² + y² = 7² so since y = 4x:

x² + (4x)² = 7²

x² + 16x² = 49

17x² = 49

x² = 49/17

x = ± √(49/17) = ± 7/√17 = ± 7√17/17

The solution in Q1 would need to be 7√17/17

So if x = 7√17/17 the y = 4(7√17/17) = 28√17/17

So the point is (7√17/17, 28√17/17)