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Oksana_A [137]
3 years ago
12

Write the equation of a circle with center (-2, 0) and area = 64 pi

Mathematics
2 answers:
agasfer [191]3 years ago
7 0
<h2>Hello!</h2>

The answer is:

The equation of the given circle is:

(x+2)^{2} +(y)^{2}=64

<h2>Why?</h2>

The equation of a circle is given by the following equation:

(x-h)^{2} +(y-k)^{2}=r^{2}

We are given the center point (-2,0) and the area of the circle.

The area of a circle is given by the formula:

A=\pi*r^{2}\\64\pi=\pi*r^{2}\\64=r^{2}

A=\pi*r^{2}\\64\pi=\pi*r^{2}\\64=r^{2}\\\sqrt{64}=r\\8=r\\r=8

So, the radius of the circle is 8 units.

Therefore,

We are given a circle where:

h=x=-2\\k=y=0\\r=8

Then, substituting into the circle equation, we have:

(x-(-2))^{2} +(y-0)^{2}=(8)^

(x+2)^{2} +(y)^{2}=64

Hence, the simplified equation of the circle is:

(x+2)^{2} +(y)^{2}=64

Have a nice day!

kozerog [31]3 years ago
5 0

Answer:

The required equation in standard form is (x+2)^2+y^2=64

Step-by-step explanation:

The equation of a circle with center (h,k) an radius, r units is given by the formula;

(x-h)^2+(y-k)^2=r^2

The given circle has center (-2,0) and radius squared can be calculated from the given area, which is 64\pi

\pi r^2=64\pi

\implies r^2=64

We substitute these values into the formula to obtain;

(x--2)^2+(y-0)^2=64

We simplify to get;

(x+2)^2+y^2=64

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