Question

I don't understand this question, please help: Write an equation of the circle whose diameter AB has endpoints A(-4,2) and B(4,-4).

Answer 1

find the midpoint of the line segment, that will be the center
do you know how to find the midpoint?

Answer 2

I think so, use the midpoint formula right?

Answer 3

right, take the average in each coordinate (i.e. add up and divide by 2)
in this case you can just about do it in your head

Answer 4

let me know what you get

Answer 5

Okay I will, hang on.

Answer 6

k

Answer 7

I got my H and K value to be (0,-1)

Answer 8

looks good

Answer 9

now we know it is going to look like
\[(x-0)^2+(y-(-1))^2=r^2\] or
\[x^2+(y+1)^2=r^2\] so we now need \(r\) right?

Answer 10

and since we have the midpoint and also a point on the circle (actually two points) we can use the distance formula to find \(r^2\)
you know the distance formula?

Answer 11

yes i know that formula, hang on so i can write this down

Answer 12

k

Answer 13

for the distance i got d to equal 100

Answer 14

seems rather unlikely
lets check

Answer 15

you want the distance between the two points \((0,-1)\) and \((4,-4)\) right?

Answer 16

oh, i messed up. the distance should have equaled 65? if I'm finding the distance between (0, -1) and (4, -4)...

Answer 17

yes, actually you do not need the distance, just the square of the distance because you need \(r^2\) not \(r\) but that is not right either
we can use the formula, but first we can think

Answer 18

from 0 to 4 is 4 units in the \(x\) direction, and from -1 to -4 is 3 units in the \(y\) direction, and so by pythagoras the square of the distance is \(3^2+4^2=9+16=25\)

Answer 19

here we are just using the old formula for a right triangle \(a^2+b^2=c^2\) which is the basis for the distance formula

Answer 20

if you want to use the distance formula it is
\[\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]
in this case you get
\[\sqrt{4-0)^2+(-1+4)^2}=\sqrt{4^2+3^2}=\sqrt{25}=5\]

Answer 21

i am not sure how you arrived at 65, but i hope it is clear what the answer is
\[r=5, r^2=25\]

Answer 22

and your "final answer" is therefore
\[x^2+(y+1)^2=25\] that is the equation for this circle