Chapter 8.4, Problem 41E

Solution

To draw: The graph of the equation $\frac{x^2}{75}+\frac{4y}{25}=0$.

Given information:

The equation $\frac{x^2}{75}+\frac{4y}{25}=0$.

Graph:

The standard form of parabola is $x^2=4py$ where the vertex is at origin $(0,0)$ , focus is at $(0,p)$ , directrix at $y=-p$ and the axis of symmetry is $x=0$.

The given equation can be written as,

  $\begin{array}{c}\frac{x^2}{75}+\frac{4y}{25}=0\\ \frac{x^2}{75}=-\frac{4y}{25}\\ \frac{x^2}{3}=-\frac{4y}{1}\\ \frac{x^2}{3}=-4y\\ x^2=3(-4y)\\ x^2=-12y\end{array}$

Here, $p=-3$.

Then, the vertex is at origin $(0,0)$ , focus is at $(0,-3)$ , directrix at $y=3$ and the axis of symmetry is $x=0$.

x	0	1	2	-1	-2
y	0	-0.083	-0.333	-0.083	-0.333

The graph is given below: