Question

The end-points of a diameter of a circle are at (−1,7) and (−3, −1). Write the equation of the circle in standard form.

A. (x+1) ² +(y−3) ² =25
B. (x+2) ² +(y−5) ² =29
C. Both a and b
D. None of the above

Answer 1

The equation of the circle with the given endpoints is (x+2)^2 + (y-3)^2 = (3sqrt(2))^2 = 18. Hence the correct answer is option D

Step-by-step explanation:

The equation of a circle with the endpoints of a diameter is given by the formula (x-h)2 + (y-k)2 = r2, where (h,k) is the center of the circle and r is the radius.

Let's find the center of the circle first. The midpoint of the diameter is the average of the x-coordinates and the average of the y-coordinates. So, (h,k) = ((-1+(-3))/2, (7+(-1))/2) = (-2, 3).

Next, let's find the radius of the circle. The radius is the distance from the center of the circle to one of the endpoints of the diameter. Using the distance formula, the radius is sqrt((-2+3)2 + (7-3)2) = sqrt(2+16) = sqrt(18) = 3sqrt(2).

Now, we can write the equation of the circle in standard form: (x+2)2 + (y-3)2 = (3sqrt(2))2 = 18.

Hence the correct answer is option D