l and m are the lengths of the tangents from the origin and the point `(9, -1)` to the circle `x^(2) + y^(2) + 18x - 2y + 32 = 0`. The value of `17(l^(2) + m^(2))` is equal to ________ .

Explanation

To solve the problem, we need to find the lengths of the tangents from the origin and the point (9, -1) to the given circle, and then calculate \( 17(l^2 + m^2) \).

### Step 1: Write the equation of the circle in standard form

The given equation of the circle is:
\[ x^2 + y^2 + 18x - 2y + 32 = 0 \]
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