Question

If one end of a diameter of the circle `x^(2) + y^(2) -4x-6y +11=0` is (3, 4), then find the coordinates of the other end of the diameter.

Answer 1

Given equation of the circle is

`x^(2)+y^(2)-4x-6y+11=0`
`therefore 2g=-4and2f=-6`
So, the centre of the circle is (-g,-f) i.e., (2,3).
Since, the mid point of AB is (2,3).
Then, `2=(3+x_(1))/2`
`rArr4=3+x_(1)`
`thereforex_(1)=1`
and `3=(4+y_(1))/2`
`rArr6=4+y_(1)rArry_(1)=2`
So, the coordinates of other end of the diameter will be (1, 2).