Question

Write the equation of a circle, in standard form, whose diameter is AB, where A=(-2,11) and B=(6,23)

Answer 1

Find the mid-point of AB. Then put it into the equation of a circle.
Standard form of a circle:
\[{(x-a)^2}+{(y-b)^2} = r^2\]
Where 'a' is the x-value of the midpoint you found, and 'b' = y-value of the midpoint you found. 'r' is just the distance from the midpoint to A or B.
So to get the mid-point you do:
\[\frac{A+B}{2}\] Which is in this case\[\frac{(-2+6, 11+23)}{2} =(a,b)\]
Then the equation of the circle will be :
\[{(x-a)^2}+{(y-b)^2} = r^2\] just replacing 'a' and 'b' with what you get for the midpoint.

Answer 2

Okay, awesome! Thanks! :D

Answer 3

Haha. No prob! You're welcome. =)