Find the focus and directrix of the parabola with the given equation. Then graph the parabola.
\[
y^{2}-24 x=0
\]
Answer
\(\boxed{\text{Final Answer: The focus of the parabola } y^{2}-24 x=0 \text{ is at } (6, 0) \text{ and the directrix is } x = -6.}\)
Step 1 ：The given equation is in the form of \(y^2 = 4ax\), where \(4a\) is the coefficient of \(x\). The focus of the parabola is at \((a, 0)\) and the equation of the directrix is \(x = -a\).
Step 2 ：To find the focus and directrix, we need to find the value of \(a\). In this case, \(4a = 24\), so \(a = 6\).
Step 3 ：The focus is at \((6, 0)\) and the directrix is \(x = -6\).
Step 4 ：The graph of the parabola is shown in the Python code output.
Step 5 ：\(\boxed{\text{Final Answer: The focus of the parabola } y^{2}-24 x=0 \text{ is at } (6, 0) \text{ and the directrix is } x = -6.}\)
