Question

Circle circumference of this equation; (x - 2)^2 + (y - 3)^2 = 16, is?

Give a full process...

Answer 1

Hey there!

We're told to find the circumference of this equation: $\bf{(x - 2)^2 + (y - 3)^2 = 16}$

To find the circumference of this equation. A given circle of a radius "r" is then required to express itself for the circumference of a circle as:

$\boxed{\bf{Circumference = 2 \times \pi \times Radius}}$

The value of radius is not given; therefore, radius is to be find via a "Circle equation" that is,

$\bf{Since, \quad (x - 2)^2 + (y - 3)^2 = 16}$

For this equation, A circles equation consists of a radius denoted as a alphabetical letter of "r" which's entered at points of "a" and "b", together as "(a, b).

$\boxed{\bf{\therefore \quad Circle \: \: Equation \: \: is: \: (x - a)^2 + (y - b)^2 = r^2}}$

Now, Rewrite this as per our Circle equation. So :: (Convert the "16" to a square of "4", this completely satisfies the equation!!)

$\bf{\therefore \quad (x - 2)^2 + (y - 3)^2 = 4^2}$

Since, A property / The properties of circle consist of the two points along with the radius, So:

$\boxed{\bf{(a, \: b) = (2, \: 3) \: \: and; \: \: \: Radius, \: \underline{r = 4}}}$

Substitute this value to get the circumference of the original Circle equation or the Equation of Circle, So:

$\bf{Since, \quad Circumference = 2 \times \pi \times Radius}$

$\bf{\therefore \quad C = 2 \times \pi \times 4}$

$\bf{\therefore \quad C = 2 \times 4 \times \pi}$

$\boxed{\bf{\underline{\therefore \quad Final \: \: Answer: \: Circumference = 8\pi}}}$

OR,

$\boxed{\bf{\underline{\therefore \quad Final \: \: Answer: \: Circumference = 25.133 \: \: \: \: [Decimal \: Form]}}}$

Hope this helps you and clears your doubts for finding the circumference of a given Circle equation!!!