a) The equation for a circle with centre (h, k) and radius r is: (x - h)^2 + (y - k)^2 = r^2
Since the centre of the circle is (0, 0), the equation for the circle with point B(5, -12) on its circumference is:
(x - 0)^2 + (y - 0)^2 = r^2
b) To determine whether point (8,10) lies inside or outside of the circle, we can substitute its coordinates into the equation for the circle.
If the equation is true, then the point lies on the circumference of the circle. If the equation is false, we can compare the left side of the equation to the right side to determine if the point is inside or outside of the circle.
For point (8,10), we can use the equation:
(x-0)^2 + (y-0)^2 = r^2
If we substitute (8,10) in the place of x and y, we get:
(8-0)^2 + (10-0)^2 = r^2
64 + 100 = r^2
164 = r^2
13 ≠ r
Since the left side of the equation is not equal to the right side, the point (8,10) lies outside of the circle.
Uday Tahlan