Question

The endpoints of a diameter of a circle are (-7, 11) and (9, -3). What is the equation of the circle?

Answer 1

See explanation.

Explanation:

Let the points be: `A=(-7,11)` and `B=(9,-3)`

To determine the equation of a circle we have to calculate:

1. The radius.
2. The coordinates of the centre.

The centre of the circle is the midpoint of its diameter. So here we can calculate the centre as:

`C=((-7+9)/2; (11+(-3))/2)=(1;4)`

To calculate the radius we can use the fact, that it is the distance between the centre and any point on the circlr:

`r=|CA|=sqrt((-7-1)^2+(11-4)^2)`

`r=sqrt(64+49)=sqrt(113)`

Now having the radius and the center we can write the equation:

`(x-1)^2+(y-4)^2=113`