Question

Q3. The circle with centre (x, y) passes through the points (3,11) (14,0) and (12,8).
Find the values of x and y.​

Answer 1

Answer:

What are the values of x and y when the circle with centre (x,y) passes through the points (3,11), (14,0) and (12,8)?

You need to find out circumcenter of triangle →

That is intersection of perpendicular bisector of any 2 side of triangle →

A(3,11),B(14,0),C(12,8)

mid point of AB (3+14/2 ,11/2 ) and slope 0–11/14–3 = -1 so slope of perpedicular

line would be 1 (m1*m2 = -1 , m1 is -1 so m2 is 2 , m1 is slope of line and m2 is slope of its perpendicular at any point)

equation of perpendicular => y-11/2 = x-17/2

y-x = -3 ….(1)

now mid point of BC → (13,4) , and slope of line 8/-2 = -4 so slope of perpendicular line would be 1/4

equation would be y-4 = 1/4 (x-13) =>

4y- x=3 ..(2)

solve equation 1 and 2 you will get center of circle ==>

( 5 ,2) , you may cross check if I missed and calculation but process remains same,

thanks for A2A