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?

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