# What is the area of the circle if the diagonal has endpoints ( 0, 3) and ( -2, 5)

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We know that the area of the circle is presented by :

A = r^2 * pi where r is the radius.

Then we will need to calculate the length of the radius.

First we will determine center which is the midpoint.

==> Mx = ( 0-2)/2 = -1

==> My = ( 3 +5)/2 = 4

Then the center is the point ( -1,4)

Now we will calculate the radius length which is the length between the center ( -1, 4) and the endpoint (0, 3)

==> r = sqrt( -1-0)^2 + ( 4-3)^2

= sqrt(1 + 1) = sqrt2

==> r = sqrt2

Now we will calculate the area.

==> A = r^2 * pi = sqrt2)^2 * pi = 2*pi = 2pi

**==> The area of the circle is A = 2pi = 6.28 square units.**

The diameter of the circle has end points ( 0,3) and ( -2, 5)

Now the diameter is sqrt [( 0+2)^2 + (3 - 5)^2]

=> sqrt [ 4 + 4]

=> 2 sqrt 2

The radius of the circle is 2 sqrt 2 / 2 = sqrt 2

The area give by pi* r^2 = pi * 2

**Therefore the required area is 2* pi.**

Question: What is the area of the circle if the **diameter** has endpoints ( 0, 3) and ( -2, 5).

Ans:

The distance between the end points of the diameter A(0,3) and B(-2, 5) is thee diameter d..

d = {(xB-XA)^2+((yB-yA)^2)}^(1/2) = {(-2-0)^2+(5-3)^2}^(1/2) = {4+4}^(1/2) = 8^(1/2).

Therefore the radius r of the circle = d/2 = 8^(1/2)}/2 = (1/2) 2*2(1/2) = 2^(1/2).

So the area of the circle = pi*r^2 = pi*{2^(1/2)}^2 = pi*2 = 2pi.

Therefore the area of the circle = 2pi = 6.2832 sq units. nearly.

**So the area of the circle = 6.2832 sq units**.