Question

a parabola is represented by the equation $x^2 = 4y$. what are the coordinates of the focus of the parabola?\
$\bigcirc\\ (0,4)$\
$\bigcirc\\ (0,1)$\
$\bigcirc\\ (1,0)$\
$\bigcirc\\ (4,0)$

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens upward or downward is \(x^{2}=4py\), where the vertex is at \((0,0)\) and the focus is at \((0,p)\).

Step2: Compare the given equation with the standard form

The given equation is \(x^{2} = 4y\). Comparing it with \(x^{2}=4py\), we can see that \(4p = 4\).

Step3: Solve for \(p\)

Divide both sides of \(4p=4\) by 4: \(p=\frac{4}{4} = 1\).

Step4: Find the focus

Since the focus of the parabola \(x^{2}=4py\) is at \((0,p)\) and \(p = 1\), the focus is at \((0,1)\).

Answer:

(0,1)