The equation `sqrt(x)=2y`, represents that graph between x and y is a :-

Options

A. Straight line
B. Parabola
C. Hyperbola
D. Circle

Answer

To determine the type of graph represented by the equation \(\sqrt{x} = 2y\), we can follow these steps:

### Step 1: Start with the given equation
The equation we have is:
\[ \sqrt{x} = 2y \]

### Step 2: Square both sides
To eliminate the square root, we square both sides of the equation:
\[ (\sqrt{x})^2 = (2y)^2 \]
This simplifies to:
\[ x = 4y^2 \]

### Step 3: Identify the form of the equation
The equation \(x = 4y^2\) is in the standard form of a parabola. The general form of a parabola that opens to the right is given by:
\[ x = ay^2 \]
where \(a\) is a constant. In our case, \(a = 4\).

### Step 4: Conclusion
Since the equation \(x = 4y^2\) represents a parabola that opens to the right, we conclude that the graph of the equation \(\sqrt{x} = 2y\) is a parabola.

### Final Answer
The graph between \(x\) and \(y\) represented by the equation \(\sqrt{x} = 2y\) is a **parabola**.

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