write the standard form of the equation of the circle for which the endpoints of a diameter are (0,0) and (4,-6)

Given:

The endpoints of a diameter are (0,0) and (4,-6).

To find:

The equation of the circle.

Solution:

The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is

Now, radius is half of the diameter.

Center of the circle is the midpoint of the endpoints of a diameter.

Standard form of a circle is

where, (h,k) is center and r is radius.

The center of the circle is (2,-3) and radius is . So,

Therefore, the standard form of the circle is .

i think it might be a but you might want a second opinion

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm