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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

Equation of a circle?

The standard equation of a circle can be expressed as:

[tex](x-a)^2+(y-b)^2 = r^2[/tex]

where;

  • (a, b) is the centre of the circle
  • r is the radius of the circle.

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

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