Question

Find an equation of the circle whose diameter has endpoints (1,-4) and (-3,6).

Answer 1

Answer:

$(x+1)^2+(y-1)^2=58$

Step-by-step explanation:

To find the equation of this circle, we must know the center and the radius.

We can find the radius by dividing the value of the distance formula by 2 (since $r=\frac{d}{2}$):

$d=\sqrt{(-3-1)^2+(6-(-4))^2}=\sqrt{116}\\r=d/2=\frac{\sqrt{116}}{2}$

We can then find the center of the circle by averaging the coordinates:

$\frac{1+(-3)}{2}=-1$

$\frac{-4+6}{2}=1$

Then, we substitute these values into the equation of a circle:

$(x-(-1))^2+(y-1)^2=(\frac{\sqrt{116}}{2})^2\\(x+1)^2+(y-1)^2=58$