Question

Given that (-4,3) and (6,-3) are opposites points on the circle (i.e diameter) write the equation of the circle

Answer 1

The center of the circle is the midpoint of the points or ((-4+6)/2,(-3+3)/2)=(1,0). Now, the diameter is the distance between the points. Using distance formulas (or noticing that the y-values are the same so it is a horizontal line), the distance is 10. Therefore, the radius is 5. The equation of a circle is (x-a)^2+(y-b)^2=r^2 where (a,b) is the center. Therefore, the equation is (x-1)^2+(y-0)^2=5^2.