Find the equation of a circle that has a diameter with the endpoints given by the points A (-5,4) and B (7,9)
In order to find the equation, we first need to find the radius and the midpoint. We can find the midpoint simply by using these equations:
(x1 + x2)/2 and (y1 + y2)/2
If we do this, we find the the midpoint is (1, 6.5)
Now, we can find the radius. To do this, we pick one of the points listed in the question and use the distance formula.
The distance formula is: √(x2 - x1)2 + (y2 - y1)2
I will just use the point (-5, 4) for this, and after plugging it in and doing some math, we find that the radius is 6.5 units.
Now we can easily find the equation of the circle. The standard form of the equation of this circle is:
(x - 1)2 + (y - 6.5)2 = 42.25
Please correct me if I'm wrong