Without rotating the original coordinate axes, to which point should origin be transferred, so that the equation `x^2 + y^2-4x + 6y-7=0` is changed to an equation which contains no term of first degree?

Answer

`(2,-3)`

Explanation

Let origin be shifted at point (h,k) without rotating the coordinate axes.
Now, we replace x by `(x+h)` and y by `(y+k)` in the equation of given curve.
Then the transformed equation is
`(x+h)^2+(y+k)^2-4(x+h)+6(y+k)-7=0`
`rArrx^2+y^2+x(2h-4)+y(2k+6)+h^2+k^2-4h+6k-7=0`
Since, this equation does not contain the terms of first degree.
`therefore 2h-4=0and 2k+6=0`
`rArrh=2and k=-3`