Pre-Calculus: Circle

Question

It has a diameter with endpoints A(-1,4) and B(4,2)

Answer 1

I assume that you are looking for the equation of the circle? If so, using the distance formula

d = sqrt( (x₂-x₁)2 + (y₂-y₁)² )

the diameter of the circle is sqrt( (2-4)² + (4+1)²) ) = sqrt(29) = 5.385

To find the midpoint of the circle, you just construct a right triangle with the points as the hypotenuse, then count halfway between the x and y coordinates on each leg.

This gives the mid-point x = 1.5 & y = 3 We know the diameter is 5.385, So the radius is 2.693

Therefore, the equation is (x-1.5)² + (y-3)² = 7.25