Final answer:
The points on the y-axis that are a distance 6 from P(5, 3) are (0, 3+√11) and (0, 3-√11), found using the distance formula and solving for the y-coordinates.
Step-by-step explanation:
To find the points on the y-axis that are a distance of 6 from point P(5, 3), we use the distance formula d = √((x2-x1)² + (y2-y1)²). Since we're looking for points on the y-axis, the x-coordinate of these points will be 0. Our formula thus simplifies to d = √((0-5)² + (y-3)²).
Substituting the distance d = 6, we get 6 = √((0-5)² + (y-3)²). Squaring both sides, we have 36 = (0-5)² + (y-3)². Since (0-5)² is 25, we simplify further: 36 = 25 + (y-3)², which leads to (y-3)² = 11. This yields two solutions: y-3 = √11 or y-3 = -√11, giving us the points (0, 3+√11) and (0, 3-√11) on the y-axis.