The equation, x²/20 + y²/20 = 1 will produce the given graph, the correct option is D.
What is a Graph?
Graph is a mathematical representation of relation between two objects.
The equations in the options are :
6x² + 6y² = 144
20x² - 20y² = 400
x² +y² =16
x²/20 + y²/20 = 1
The graph represents a circle, and the standard equation of a circle is given by,
(x -h)² + (y-k)² = r²
(h,k) is the center of the circle.
The equation 6x² + 6y² = 144 can be written as
⇒x² + y² = 144/6
x² + y² = 24
Comparing this with the standard equation of the circle
h = 0, k = 0 , r = 4.89
⇒ 20x² - 20y² = 400, this represents a hyperbola
⇒ x² +y² =16 , this is a circle
h = 0, k = 0 , r = 4
⇒ x²/20 + y²/20 = 1
x² +y² = 20, this is a circle
h = 0, k = 0 , r = 4.47
The graphs are plotted for the three circle, but the radius of the circle in the figure is in between 4 and 5 approximately equal to 4.5, which is represented by x² +y² = 20.
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