Question

Square RSTU is inscribed in circle P. Given the coordinates for the vertices of the square, find the equation of circle P.
R(0, 4), S(6, 2), T(4, -4), and U(-2, -2)

(x - 2)2 + y2 = 68
(x + 2)2 + y2 = 20
(x - 2)2 + y2 = 20

Answer 1

well since the square is inside the circle...

find the midpoint of a diagonal... that will be the centre of the circle..

then you can find the equation.

to check find the midpoint of the other diagonal... and it should be the same point as the
1st diagonal...

the reason is that diagonals in a square bisect each other.

hope it helps

Answer 2

now one of the vertices of the square is on the circumference of the circle.

so substitute a point into your equation to find r^2

then you'll have the correct answer

Answer 3

K

Answer 4

2,0 is the midpoint @campbell_st

Answer 5

i need help finding radius though

Answer 6

great so the general equation is

\[(x - h)^2 + (y - k)^2 = r^2\]

where (h, k) is the centre

so using your midpoint the equation is

\[(x -2)^2 + (y - 0)^2 = r^2\]

to find the value of r^2 substitute a point that is a vertex... as it's on the circumference

then you'll have all the bits for the equation

it doesn't matter which vertex you choose

Answer 7

ok

Answer 8

so 20 @campbell_st

Answer 9

correct... so do you have an answer choice that matches... ?

Answer 10

C

Answer 11

CC

Answer 12

thxs