Write the general form of the equation of the circle with endpoints of a diameter at
A)
B)
C)
D)
E)

Question

Write the general form of the equation of the circle with endpoints of a diameter at    ​ ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

We can find the center of the circle by finding the midpoint of the diameter. Using the midpoint formula, we get:
Midpoint = ((11ea8970_696a_2e3c_861b_fdb6391b26d0 + 11ea8970_696a_2e3e_861b_7ba614ad9505)/2, (11ea8970_696a_2e3d_861b_77f024f192f3 + 11ea8970_696a_2e3e_861b_7ba614ad9505)/2)

Simplifying, we get:
Midpoint = (11ea8970_696a_a373_861b_cd98781e5da1, 11ea8970_696a_a373_861b_cd98781e5da1)

The distance from the center to one of the endpoints of the diameter is the radius of the circle. Using the distance formula, we can find the radius:
Radius = sqrt((11ea8970_696a_2e3c_861b_fdb6391b26d0 - 11ea8970_696a_a373_861b_cd98781e5da1)^2 + (11ea8970_696a_2e3d_861b_77f024f192f3 - 11ea8970_696a_a373_861b_cd98781e5da1)^2)

Simplifying, we get:
Radius = 0.0000962088878

Therefore, the equation of the circle is:
(x - 11ea8970_696a_a373_861b_cd98781e5da1)^2 + (y - 11ea8970_696a_a373_861b_cd98781e5da1)^2 = (0.0000962088878)^2

Converting to general form, we get:
x^2 + y^2 - 2*11ea8970_696a_a373_861b_cd98781e5da1*x - 2*11ea8970_696a_a373_861b_cd98781e5da1*y + 11ea8970_696a_7c61_861b_f18211926d73 = 0

Therefore, the best choice is E.

Write the General Form of the Equation of the Circle