Points `A(-1, y)` and `B(5, 7)` lie on a circle with centre `O(2, -3y)` . Find the values of y. Hence, find the radius of the circle.

Explanation

To solve the problem, we need to find the values of \( y \) such that the points \( A(-1, y) \) and \( B(5, 7) \) lie on the same circle with center \( O(2, -3y) \). The key idea is that the distances from the center \( O \) to points \( A \) and \( B \) must be equal.

### Step 1: Write the distance formulas
The distance from the center \( O(2, -3y) \) to point \( A(-1, y) \) is given by:
\[ OA = \sqrt{(2 - (-1))^2 + (-3y - y)^2} = \sqrt{(2 + 1)^2 + (-4y)^2} = \sqrt{3^2 + 16y^2} = \sqrt{9 + 16y^2} \]

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