Question 1209662
To find the conic section represented by the equation y² + 3x + 11y + 18 = -x² - 17y + 59, we need to simplify and rearrange the equation into a standard form.

1. **Combine like terms and move all terms to one side:**
   y² + 3x + 11y + 18 + x² + 17y - 59 = 0
   x² + 3x + y² + 28y - 41 = 0

2. **Complete the square for both x and y terms:**
   (x² + 3x + (3/2)²) + (y² + 28y + 14²) - 41 - (3/2)² - 14² = 0
   (x + 3/2)² + (y + 14)² - 41 - 9/4 - 196 = 0
   (x + 3/2)² + (y + 14)² - (164 + 9 + 784)/4 = 0
   (x + 3/2)² + (y + 14)² - 957/4 = 0
   (x + 3/2)² + (y + 14)² = 957/4

3. **Analyze the equation:**
   The equation is now in the standard form of a circle:
   (x - h)² + (y - k)² = r²

In our case, the equation is:
(x + 3/2)² + (y + 14)² = 957/4

This is the equation of a circle with center (-3/2, -14) and radius √(957/4) = √957 / 2.

Therefore, the conic section represented by the given equation is a **circle**.