# A circle has a centre at (-3, 1) and point P(0, 5) is on the circle. What is the area of the circle,in units squared?

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To calculate the area (a) of the circle you need to determine the radius (r):

a= pi* r^2 (pi= 3.14)

Now to calculate the radius, we have the segment (-3,1) and (0,5) represents the radius.

Now we need to calculate the distance between both points:

The formula for the distance between two point is:

d= sqrt[(x2-x1)^2 + (y2-y1)^2]

d= sqrt[(0-(-3)^2 + (5-1)^2]

= sqrt(9+16)

= sqrt(25)

= 5

Then the radius r= 5

Then the area s= pi*25 = 3.14*25= 78.5

We notice that using the formula of the area of the circle, we do not know the value of the raidus.

A = pi*r^2, where pi=3.14 and r is the radius of the circle.

From enunciation, we know the coordinates of 2 points which are the center of the circle and a point located on the circle.

The length of the segment which joins the 2 points is the radius of the circle.

To calculate the length of the segment, we'll apply the formula:

r = sqrt[(0+3)^2 + (5-1)^2]

r = sqrt(9+16)

r = sqrt25

r = 5

Now, we'll substitute the radius by it's value in the formula of the Area:

A = pi*5^2

A = pi*25

A = 3.14*25

**A = 78.5 square units**

The centre and a point on the circumference determines the radius of the circle by their distance. The distance d between two points (x1,y1) and (x2,y2) is given by d = sqrt{(x2-x1)^2+(y2-y1)^2}.

Here (x1,y1) = centre(_3,1) and P(0,5).

Therefore the radiusr = CP = sqrt{((0--3)^2+(5-1)}^2} = sqrt((9+16} = srt25 = 5.

So the area of this circle = pi*radius^2= pi*5^2= 25pi

The radius of the circle is equal to the distance between its center and any point on the circle.

For the given circle the center is at (-3, 1) and a point on it is P(0, 5).

Therefore the radius of the circle is equal to the distance between these two points. To calculate the distance we use the formula:

Distance = [(y2 - y1)^2 + (x2 - x1)^2]^1/2

Where the coordinates of two points are (x1, y1) and (x2, y2)

Thus distance between center and point P = Radius

= [(5 - 1)^2 + (0 +3)^2]^1/2

= (4^2 + 3^2)^1/2

= (16 + 9)^1/2

= 25^1/2 = 5

Now we calculate the area of the circle using the formula:

Area = pi*r^2

Where:

pi = a constant with value equal to 22/7

r = radius of circle

Substituting values of pi and r in the equation for area we get:

Area = (22/7)*5^2 = (22/7)*25 = 78.5714 (unit of length)^2