Problem

Find the vertex, focus, and directrix of the parabola given by the equation \(y^2 = 4x\).

Solution

Step 1 :Step 1: Rewrite the given equation in standard form for a parabola. The standard form of a parabola is \(y^2 = 4px\), where \(p\) is the distance from the vertex to the focus.

Step 2 :Step 2: From the standard form, we can identify that \(4p = 4\), hence \(p = 1\).

Step 3 :Step 3: The vertex of the parabola is at the origin, \((0,0)\), because the equation is already in standard form.

Step 4 :Step 4: The focus of the parabola is \((p,0)\), substituting \(p = 1\) we get the focus as \((1,0)\).

Step 5 :Step 5: The directrix of the parabola is \(x = -p\), substituting \(p = 1\) we get the directrix as \(x = -1\).

From Solvely APP
Source: https://solvelyapp.com/problems/sr5147EnBm/

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