The equation of a tangent to the circle with centre `(2, -1)` is `3x + y = 0`. Twice of the square of the length of the tangent to the circle from the point `(23, 17)` is __________ .

Explanation

To solve the problem, we need to find twice the square of the length of the tangent from the point (23, 17) to the circle with center (2, -1) and a tangent line given by the equation \(3x + y = 0\).

### Step 1: Find the radius of the circle

The distance from the center of the circle to the tangent line can be calculated using the formula for the perpendicular distance from a point to a line. The line can be expressed in the form \(Ax + By + C = 0\), where \(A = 3\), \(B = 1\), and \(C = 0\).

The center of the circle is at the point \((2, -1)\). The formula for the distance \(d\) from a point \((x_1, y_1)\) to a line \(Ax + By + C = 0\) is given by:

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