What is the equation of a circle that passes through points: (1,2), (-1,-1), and (3,1)?

Question

Show work to solve for the center coordinate (x,y) and give equation showing the radius.

Answer 1

Let (x,y) be the center. The squares of the distances between your points and the center are

(x-1)^2 + (y-2)^2 = x^2 + y^2 - 2x - 4y + 5
(x+1)^2 + (y+1)^2 = x^2 + y^2 + 2x + 2y + 2
(x-3)^2 + (y-1)^2 = x^2 + y^2 - 6x - 2y + 10

These should be equal to the square of the radius and therefore to each other. Cancelling the terms x^2 + y^2, we find

-2x - 4y + 5 = 2x + 2y + 2 = -6x - 2y + 10

Subtracting the first from the second and the third from the second, I get

4x + 6y - 3 = 0
8x + 4y - 8 = 0

Subtract twice the first equation from the second,

-8y - 2 = 0
so y = -1/4; it follows that x = 9/8.

Check:
(x-1)^2 + (y-2)^2 = (1/8)^2 + (-9/4)^2 = 325/64
(x+1)^2 + (y+1)^2 = (17/8)^2 + (3/4)^2 = 325/64
(x-3)^2 + (y-1)^2 = (-15/8)^2 + (5/4)^2 = 325/64

THe radius is sqrt(325/64) = 5/8 * sqrt(13).

Answer 2

Everyone can use a little tutoring from time to time, looks like arwyayen23 could use some in his socal skills. Now then, take the values graciously supplied by others and make an equation that looks something like this:

(x-9/8)^2+(y+1/4)^2=(squrt325/ 64)^2

y1=[+ {squrt(squrt325/64)^2-(x-9/8) ^2 }] - (1/4)
y2=[- " " " ] ( " )


Put that on your TI-84 Plus, and you should be able to see the graph and the coordinate table.

Answer 3

Line connecting (-1,-1) - (3,1) line segment:

2y - x = -1 => y = 0.5(x-1)
Line bisecting this segment: m = -2
point: (1,0) => y = -2x + 2


Line connecting (-1,-1) - (1,2) line segment:

y = 1.5x + 0.5
Line bisecting this point m= -(2/3)

point (0, 0.5) => y = -(2/3)x + .5

y = y

-2x + 2 = -(2/3)x + 0.5

1.5 = (4/3)x

x = 1.125

=> y = -.25
center = (1.125,-.25)

Use pythagorus to find radius between center and point.

(X-Xc)^2 + (Y-Yc)^2) = r^2

Answer 4

properly, the tangent is going to have a perpendicular slope, so opposite reciprocal slope. y = -5/12x + b a million = -5/12(3) + b a million = -15/12 + b b = 2 a million/4 y = -5/12x + 2 a million/4 12y = -5x + 27 5x + 12y = 27

Answer 5

it might help if you try to sketch it. the equation for a circle is < X squared + Y squared = radius squared> . try sub. the points into the equation and solving for it. it might work.

Answer 6

above are decent answer, but the correct answer is:

Do your own homework!

Answer 7

good answer DutchProf