Question

The center of the circle that passes through the points (-2,3), (0,-3), and (4,-3) is________
a) (2,2)
b) there is not enough data to find the center
c) (1,2)
d) (2,1)

Answer 1

first we can find the eq of circle passing through three points, then can check the centre

Answer 2

how do I do that?

Answer 3

general eq of the circle is
\[x^2+y^2+2gx+2fy+c=0\]

Answer 4

substitute the three points in this eq
we get three eqs in three unknows
find the unknows g,f and c

Answer 5

centre is
\[\sqrt{g^2+f^2-c}\]

Answer 6

for(-2,3)
4+9-4g+6f+c=0

Answer 7

for(0,-3)
9-6f+c=0

Answer 8

for(4,-3)
16+9+8g-6f+c=0

Answer 9

-4g+6f+c=-13
-6f+c=-9
8g-6f+c=-25

Answer 10

subtracting 1 n 3

-12g+12f=12
-g+f=1

Answer 11

sub 1 n 2
-4g+12f=-4
g-3f=1

Answer 12

adding the resultant eqs
-2f=2
f=-1
which gives
g=-2
n
c=-3

Answer 13

center=(-g,-f)=(2,1)

Answer 14

so D is the right option:)

Answer 15

m sorry
the formula i wrote earlier is to find the radius

Answer 16

thank you for your help

Answer 17

u got all the lenghy computations?

Answer 18

lengthy*

Answer 19

for the most part

Answer 20

what do g and f represent though?

Answer 21

if there is some confusion, u can ask:)

Answer 22

these r constants

Answer 23

the eq i wrote is the general eq of the circle

Answer 24

finding out g,f and c, we can find the eq of the circle

Answer 25

okay thank you

Answer 26

welcome:)