Question

A circle has its center at (1,-3). One point on the circle is (5,-6). Which is another point the lies on the circle?

a. (-3,2)
b. (4,6)
c. (0,5)
d. (-2,-7)

Answer 1

To find another point on the circle, we can use the equation of a circle and substitute values to solve for the unknowns.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2. In this case, the center of the circle is (1, -3) and a point on the circle is (5, -6). Substituting these values, we can find the equation of the circle: (x - 1)^2 + (y + 3)^2 = r^2. To find another point on the circle, we can substitute values into this equation and solve for the unknowns. Let's substitute the values from option B, (4, 6):

(4 - 1)^2 + (6 + 3)^2 = r^2
9 + 81 = r^2
90 = r^2

So, the point (4, 6) lies on the circle.