Question

which is the focus of a parabola with equation $y^2 = 4x$?
$(0, -1)$ $(0, 1)$ $(1, 0)$
$(-1, 0)$

Explanation:

Step1: Recall parabola standard form

The standard form of a parabola that opens to the right is \(y^{2}=4px\), where the focus is at \((p,0)\).

Step2: Compare with given equation

Given the equation \(y^{2}=4x\), we can compare it with \(y^{2}=4px\). Here, \(4p = 4\), so solving for \(p\) gives \(p = 1\).

Step3: Determine the focus

Since the parabola \(y^{2}=4px\) has focus \((p,0)\) and \(p = 1\), the focus is \((1,0)\).

Answer:

\((1, 0)\)