which of the following equations will produce the graph shown below?
![which of the following equations will produce the graph shown below class=](https://us-static.z-dn.net/files/d8c/f508c568ef359c5c0ea8ced5bbc54993.jpg)
Answer:
Option (B) is correct.
[tex]\frac{x^2}{20}+\frac{y^2}{20}=1[/tex] equation will produce the graph shown.
Step-by-step explanation:
Given a graph showing circle .
We have to determine the equation that will produce the graph shown.
Consider the given graph.
It shows a circle with radius 4.5
The general equation of circle is represented by [tex]x^2+y^2=r^2[/tex]
Since option (A) represents the equation of hyperbola.
Option (C) represents the equation of circle with radius 4, but the given graph has radius grater than 4 .
Option (D) can be rewritten as by dividing by 6,
[tex]x^2+y^2=\frac{144}{6}=24[/tex] which is a equation of circle with radius 4.9 (approx)
Thus, only Option (B) works for the given graph.
[tex]\frac{x^2}{20}+\frac{y^2}{20}=1[/tex]
Multiply , by 20 , we get,
[tex]x^2+y^2=20[/tex] also, [tex]\sqrt{20}=4.47(approx)[/tex]
Thus, Option (B) is correct.
[tex]\frac{x^2}{20}+\frac{y^2}{20}=1[/tex]
The equation 6x² + 6y² = 144 is correct
The standard equation of a circle can be expressed as:
[tex](x-a)^2+(y-b)^2 = r^2[/tex]
where;
From the diagram, we can see that the radius of the circle is between 4 and 5. Hence the correct equation must have a radius between these values
From the option, we can see that the only equation that will have a radius between 4 and 5 is [tex]6x^2+6y^2=144[/tex]
Divide through by 6:
[tex]x^2+y^2 =\frac{144}{6}\\x^2+y^2= 24\\x^2+y^2=(\sqrt{24})^2[/tex]
Since the square root of 24 is between 4 and 5, hence the equation 6x² + 6y² = 144 is correct
Learn more on equation of a circle here: https://brainly.com/question/1506955