Answer:
[tex]x^2 + y^2 = 1273885[/tex]
Step-by-step explanation:
Given
[tex]Area = 4000000[/tex]
[tex](h,k) =(0,0)[/tex]
Required
The equation of the circle
First, we calculate the radius of the circle using;
[tex]Area = \pi r^2[/tex]
This gives:
[tex]4000000= \pi r^2[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]\frac{4000000}{\pi}= r^2[/tex]
Take [tex]\pi[/tex] as 3.14
[tex]\frac{4000000}{3.14}= r^2[/tex]
[tex]1273885.35032= r^2[/tex]
Approximate
[tex]1273885= r^2[/tex]
Rewrite as:
[tex]r^2 = 1273885[/tex]
The equation of the circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where:
[tex](h,k) =(0,0)[/tex]
[tex]r^2 = 1273885[/tex]
So, we have:
[tex](x - 0)^2 + (y -0)^2 = 1273885[/tex]
Open brackets
[tex]x^2 + y^2 = 1273885[/tex]
(c) is correct.
The difference in [tex]x^2 + y^2 = 1273885[/tex] and (c) in the question is due to approximation
