+0

# Coordinates

+1
15
1
+359

Find the coordinates of the center of the circle.

Jan 13, 2024

#1
+36919
+1

Using distance formula, the distance^2 from a,b to each of the points on the circle is the same ....

to 2,0 and 7,1 :

(a-2)^2 + (b-0)^2  = (a-7)^2 + (b-1)^2       simplify to

10a+2b = 46

to  2,0 and 3,5

( a-2)^2  + ( b-0)^2  = (a-3)^2 + (b-5)^2    simplify to

2a +10b = 30

Now you have two equations relating two unknowns....solve for a and b

Multiply top equation by -5 to get

-50a - 10 b = -230    and add it to the second equation to get

-48a = -200

a = 4.167.      use this value of 'a' in one of the equatins to find  b = 2.167

Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024

#1
+36919
+1

Using distance formula, the distance^2 from a,b to each of the points on the circle is the same ....

to 2,0 and 7,1 :

(a-2)^2 + (b-0)^2  = (a-7)^2 + (b-1)^2       simplify to

10a+2b = 46

to  2,0 and 3,5

( a-2)^2  + ( b-0)^2  = (a-3)^2 + (b-5)^2    simplify to

2a +10b = 30

Now you have two equations relating two unknowns....solve for a and b

Multiply top equation by -5 to get

-50a - 10 b = -230    and add it to the second equation to get

-48a = -200

a = 4.167.      use this value of 'a' in one of the equatins to find  b = 2.167

ElectricPavlov Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024