Question

4) Find the standard form of the equation of a circle

with endpoints of a diameter at (0,0) and
solution point (-4, 6).

Answer 1

The standard form of the equation of a circle with endpoints of a diameter at (0,0) and solution point (-4, 6) is (x+2)^2 + (y-3)^2 = 13.

Step-by-step explanation:

The standard form of the equation of a circle with endpoints of a diameter at (0,0) and solution point (-4, 6) can be found using the midpoint formula.

First, we find the midpoint of the diameter by taking the average of the x-coordinates and the average of the y-coordinates.

The midpoint is (0-4)/2, (0+6)/2 = -2, 3. The radius of the circle is the distance between the midpoint and one of the endpoints. Using the distance formula, we have

r = sqrt((-2-(-4))^2 + (3-6)^2) = sqrt(4 +9) = sqrt(13).

Hence, the standard form of the equation of the circle is (x+2)^2 + (y-3)^2 = 13.