Question

what is the focus of a parabola with equation y = 50x²?
a. (0, 1/200)
b. (0, 25/2)
c. (0, 50)
d. (0, 200)

Explanation:

Step1: Rewrite in standard form

The standard - form of a parabola is \(x^{2}=4py\). Given \(y = 50x^{2}\), we can rewrite it as \(x^{2}=\frac{1}{50}y\).

Step2: Find the value of \(p\)

Comparing \(x^{2}=\frac{1}{50}y\) with \(x^{2}=4py\), we have \(4p=\frac{1}{50}\). Solving for \(p\), we get \(p=\frac{1}{200}\).

Step3: Determine the focus

For a parabola of the form \(x^{2}=4py\) with its vertex at the origin \((0,0)\), the focus is at the point \((0,p)\). Since \(p = \frac{1}{200}\), the focus is \((0,\frac{1}{200})\).

Answer:

A. \((0,\frac{1}{200})\)