Question
What is the equation of a circle with a center of (2,-4) that passes through the point (4,-6)(1 point)
Answers
GPT 3.5
The general equation of a circle with a center at (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.
Given that the center is (2, -4) and the point (4, -6) is on the circle, we can substitute these values into the equation of the circle:
(x - 2)^2 + (y + 4)^2 = r^2
Now, we substitute the point (4, -6) into the equation:
(4 - 2)^2 + (-6 + 4)^2 = r^2
2^2 + (-2)^2 = r^2
4 + 4 = r^2
8 = r^2
Therefore, the equation of the circle is (x - 2)^2 + (y + 4)^2 = 8.
Given that the center is (2, -4) and the point (4, -6) is on the circle, we can substitute these values into the equation of the circle:
(x - 2)^2 + (y + 4)^2 = r^2
Now, we substitute the point (4, -6) into the equation:
(4 - 2)^2 + (-6 + 4)^2 = r^2
2^2 + (-2)^2 = r^2
4 + 4 = r^2
8 = r^2
Therefore, the equation of the circle is (x - 2)^2 + (y + 4)^2 = 8.