Final answer:
The minimum integral value of k in the given hyperbola equation is 1.
Step-by-step explanation:
The given equation represents a hyperbola. To find the minimum integral value of k, we need to analyze the equation further.
By comparing it to the standard form of a hyperbola, (x-h)²/a² - (y-k)²/b² = 1, we can see that:
- a² = k²(3x+y+2)²/100
- b² = k²
Since a hyperbola is symmetrical, its minimum value of k occurs when the smaller denominator between a² and b² is chosen. In this case, b² = k², so the minimum integral value of k is 1.