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

Answer:

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

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

Step-by-step 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:

$Area = \frac{\theta}{360} * \pi r^2$

So, we have:

$Area = \frac{30}{360} * 3.14 * 8^2$

$Area = \frac{1}{12} * 200.96$

$Area = 16.75cm^2$