in the standard (x,y) coordinate plane, what is the area of the circle x^2 + y^2 =169?

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elliottou elliottou · Answer 1 · 2020-04-30T19:41:37+02:00

Answer:

169π

Step-by-step explanation:

circle eq: (x-a)²+(y-b)²=r², where (a,b) is center and r is radius

r²=169

r = ±13

since a radius length must be positive, r = +13, not -13

A of circle: πr²

r = 13

169π

given that the circle eq has r², you could've noticed that you can take the constant in the circle eq and multiply that by π to get the same answer

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MrRoyal MrRoyal · Answer 2 · 2021-11-30T12:08:00+01:00

The area of the circle is 530.66 square units

The equation of the circle is given as:

[tex]\mathbf{x^2 + y^2 = 169}[/tex]

Express 169 as 13^2

[tex]\mathbf{x^2 + y^2 = 13^2}[/tex]

The equation of a circle is represented as:

[tex]\mathbf{x^2 + y^2 = r^2}[/tex]

Where r is the radius.

So, by comparison:

[tex]\mathbf{r = 13}[/tex]

The area of a circle is:

[tex]\mathbf{Area = \pi r^2}[/tex]

So, we have:

[tex]\mathbf{Area = 3.14 \times 13^2}[/tex]

[tex]\mathbf{Area = 530.66}[/tex]

Hence, the area of the circle is 530.66 square units