Equation of directrix of parabola ` 5y^(2) = 4x ` is

Options

A. `4x - 1 = 0`
B. `4x + 1 = 0`
C. `5x + 1 = 0`
D. `5x - 1 = 0`

Answer

To find the equation of the directrix of the parabola given by the equation \(5y^2 = 4x\), we can follow these steps:

### Step 1: Rewrite the equation in standard form
The given equation is \(5y^2 = 4x\). We can rewrite it in the standard form of a parabola, which is \(y^2 = 4Ax\).

To do this, we divide both sides by 5:
\[ y^2 = \frac{4}{5}x \]

### Step 2: Identify the value of \(A\)
From the standard form \(y^2 = 4Ax\), we can see that \(4A = \frac{4}{5}\). To find \(A\), we divide both sides by 4:
\[ A = \frac{1}{5} \]

### Step 3: Write the equation of the directrix
The equation of the directrix for a parabola that opens to the right is given by \(x = -A\). Substituting the value of \(A\) we found:
\[ x = -\frac{1}{5} \]

### Step 4: Convert to standard form
To express this in standard form, we can multiply both sides by 5:
\[ 5x + 1 = 0 \]

Thus, the equation of the directrix is:
\[ 5x + 1 = 0 \]

### Final Answer
The equation of the directrix of the parabola \(5y^2 = 4x\) is:
\[ 5x + 1 = 0 \]

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