Question

Write an equation for a circle in standard form with a center at (-6, 5) and has a radius equal to 5. 2 Find the area of the sector if the radius is 8cm show your work below 2 2 Show your work below. You have responded to 0 of 7 questions. Question Details Write an equation for a circle in standard form with a center at (-6, 5) and has a radius equal to 5.

Answer 1

`(a)\ (x+6)^2 + (y-5)^2 = 25`

`(b)\ Area = 16.75cm^2`

Explanation:

Solving (a):

Given

`(a,b) = (-6,5)`

`r = 5`

Required

The equation of the circle

This is calculated as:

`(x-a)^2 + (y-b)^2 = r^2`

So, we have:

`(x--6)^2 + (y-5)^2 = 5^2`

`(x+6)^2 + (y-5)^2 = 25`

Solving (b):

Given

`r = 8cm`

`\theta = 30^o` --- Missing from the question

Required

The area of the sector

This is calculated using:

`Area = (\theta)/(360) * \pi r^2`

So, we have:

`Area = (30)/(360) * 3.14 * 8^2`

`Area = (1)/(12) * 200.96`

`Area = 16.75cm^2`