The equation of the parabola whose vertex is origin axis along x-axis and which passes through the point (-2,4) is

Options

A. `y^(2)=-8x `
B. `y^(2)=8x `
C. `x^(2)=16x`
D. `x^(2)=8y`

Answer

To find the equation of the parabola with the given conditions, we will follow these steps:

### Step 1: Identify the standard form of the parabola
Since the vertex of the parabola is at the origin (0,0) and the axis is along the x-axis, the standard form of the equation of the parabola is:
\[ y^2 = 4ax \]
where \(a\) is the distance from the vertex to the focus.

### Step 2: Use the given point to find the value of \(a\)
We know that the parabola passes through the point (-2, 4). We will substitute \(x = -2\) and \(y = 4\) into the equation \(y^2 = 4ax\):
\[ 4^2 = 4a(-2) \]
This simplifies to:
\[ 16 = -8a \]

### Step 3: Solve for \(a\)
Now, we can solve for \(a\):
\[ -8a = 16 \implies a = -2 \]

### Step 4: Substitute \(a\) back into the equation
Now that we have the value of \(a\), we can substitute it back into the standard form of the parabola:
\[ y^2 = 4(-2)x \]
This simplifies to:
\[ y^2 = -8x \]

### Final Answer
Thus, the equation of the parabola is:
\[ \boxed{y^2 = -8x} \]

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