Find the name of the conic represented by `sqrt((x/a))+sqrt((y/b))=1`.

Answer

To find the name of the conic represented by the equation \( \sqrt{\frac{x}{a}} + \sqrt{\frac{y}{b}} = 1 \), we will follow a series of steps to manipulate the equation and identify the conic section.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ \sqrt{\frac{x}{a}} + \sqrt{\frac{y}{b}} = 1 \]

2. **Isolate one of the square root terms:**
\[ \sqrt{\frac{y}{b}} = 1 - \sqrt{\frac{x}{a}} \]

3. **Square both sides to eliminate the square root:**
\[ \frac{y}{b} = (1 - \sqrt{\frac{x}{a}})^2 \]

4. **Expand the right-hand side:**
\[ \frac{y}{b} = 1 - 2\sqrt{\frac{x}{a}} + \frac{x}{a} \]

5. **Multiply through by \( b \) to eliminate the fraction:**
\[ y = b(1 - 2\sqrt{\frac{x}{a}} + \frac{x}{a}) \]

6. **Distribute \( b \):**
\[ y = b - 2b\sqrt{\frac{x}{a}} + \frac{bx}{a} \]

7. **Rearrange the equation:**
\[ y - \frac{bx}{a} + 2b\sqrt{\frac{x}{a}} - b = 0 \]

8. **Isolate the square root term:**
\[ 2b\sqrt{\frac{x}{a}} = b - y + \frac{bx}{a} \]

9. **Square both sides again to eliminate the square root:**
\[ 4b^2 \cdot \frac{x}{a} = (b - y + \frac{bx}{a})^2 \]

10. **Expand the right-hand side:**
\[ 4b^2 \cdot \frac{x}{a} = (b - y)^2 + 2(b - y)\frac{bx}{a} + \left(\frac{bx}{a}\right)^2 \]

11. **Rearrange the equation to standard conic form:**
\[ 4b^2 \cdot \frac{x}{a} - (b - y)^2 - 2(b - y)\frac{bx}{a} - \left(\frac{bx}{a}\right)^2 = 0 \]

12. **Identify the conic section:**
The resulting equation can be analyzed using the general conic section form. By comparing coefficients, we can determine the type of conic.

After analysis, we find that the relationship between the coefficients satisfies the condition for a parabola.

### Conclusion:
The conic represented by the equation \( \sqrt{\frac{x}{a}} + \sqrt{\frac{y}{b}} = 1 \) is a **parabola**.