Question

Which of the following equations will produce the graph shown below?

Answer 1

The graph is a circle, centered at the origin, with radius=4.

We know that we can write the equation of a circle with radius r and center (a,b) as :

                      $(x-a)^2+(y-b)^2=r^2$.

Thus, substituting (a, b) with (0, 0) and r with 4, we have:

                      $x^2+y^2=16$.

The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:

$x^2+y^2=16\\\\x^2+y^2-16=0\\\\2(x^2+y^2-16)=0$, 

we would still have the same roots.

Thus, the equation of the circle can be written as :

                                    $2x^2+2y^2=32$.


Answer: B

Answer 2

The equation of the circle with a radius of 4 and the centre at origin is x² + y² = 16

How to find the equation of a circle

The standard equation of a circle is expressed as:
(x - a)² + (y- b)² = r²

where:

(a, b) is the centre of the circle

r is the radius

From the given circle

(a, b) = (0, 0)

r = 4 units

Substitute

(x - 0)² + (y- 0)² = 4²

x² + y² = 16

Hence the equation of the circle with a radius of 4 and the centre at origin is x² + y² = 16

Learn more on equation of a circle here: https://brainly.com/question/1506955