Find the condition that the point (h, k) may lie on the curve `x^(2)+y^(2)+5x+11y-2=0`.

Answer

To find the condition that the point \((h, k)\) may lie on the curve given by the equation

\[ x^2 + y^2 + 5x + 11y - 2 = 0, \]

we can follow these steps:

### Step 1: Substitute the point \((h, k)\) into the equation
We need to check if the point \((h, k)\) satisfies the equation of the curve. We substitute \(x = h\) and \(y = k\) into the equation:

\[ h^2 + k^2 + 5h + 11k - 2 = 0. \]

### Step 2: Rearranging the equation
Rearranging the equation gives us:

\[ h^2 + k^2 + 5h + 11k = 2. \]

### Step 3: Identify the condition
This equation represents the condition that must be satisfied for the point \((h, k)\) to lie on the curve.

### Final Condition
Thus, the condition for the point \((h, k)\) to lie on the curve is:

\[ h^2 + k^2 + 5h + 11k - 2 = 0. \]