Final answer:
To find the values of a and b, we use the distance formula between points P and Q and the given condition, PQ = a2 + b2, to set up an equation that can be solved for a and b.
Step-by-step explanation:
The question asks to find the values of a and b for the point Q(a, b) in the number plane, such that the distance PQ is equal to a2 + b2, where P is the point (2,3). To solve this, we use the distance formula between two points P(x1, y1) and Q(x2, y2), given by the square root of ((x2 - x1)2 + (y2 - y1)2). In this case, PQ is the distance between P(2, 3) and Q(a, b), therefore PQ = sqrt((a - 2)2 + (b - 3)2).
Since we are given that PQ = a2 + b2, we can equate the two expressions to sqrt((a - 2)2 + (b - 3)2) = sqrt(a2 + b2). Squaring both sides to remove the square root gives (a - 2)2 + (b - 3)2 = a2 + b2. Expanding and simplifying further can lead us to the solution of a and b.