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3 years ago

Write the equation of a circle with center (4,5) and a Circumference = 16 pi

Mathematics

2 answers:

3241004551 [841]3 years ago

8 0

Answer:

The required equation in standard form is $(x-4)^2+(y-5)^2=64$

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 (4,5) and the radius can be calculated from the given circumference, which is $C=16\pi$

$2\pi r=16\pi$

$\implies r=8$

We substitute these values into the formula to obtain;

$(x-4)^2+(y-5)^2=8^2$

We simplify to get;

$(x-4)^2+(y-5)^2=64$

jasenka [17]3 years ago

5 0

Answer:

Equation of the circle : (x - 4)² + (y - 5)² = 64

Step-by-step explanation:

Equation of the circle

(x - x₁)² + (y - y₁)² = r²

Where (x₁, y₁) be the coordinates of center and r is the radius of circle.

<u>To find the radius</u>

It is given that circumference of circle = 16π

Circumference 2πr = 16

r = 16π/2π= 8

<u>To find the equation of the circle</u>

Center = (4, 5)

(x - x₁)² + (y - y₁)² = r²

(x - 4)² + (y - 5)² = 8²

(x - 4)² + (y - 5)² = 64

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Answer:

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Step-by-step explanation:

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