InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find a point at which origin is shifted such that transformed equation of x^(2)+xy-3x-y+2=0 has no first degree term and constant term. Also find the transformed equation. |
|
Answer» Solution :LET origin be shifted to the point `(h,k)`. `:. "Put" X=X+h` and `y=Y+k` `(X+h)^(2)+(X+h)(Y+k)-3(X+h)-(Y+k)+2=0` `implies X^(2)+2hX+h^(2)+XY+hY+kX+hk-3X-3h-Y-k+2=0` `impliesX^(2)+XY+X(2h+k-3)+Y(h-1)+(h^(2)+hk-3h-k+2)=0`……`(1)` This EQUATION will be independent with first degree term and constant term if `{:(,2h+k-3=0),(,h-1=0),("and",h^(2)+hk-3h-k+2=0):}}impliesh=1,k=1` `:.` Required point `=(1,1)` and transformed equation is `X^(2)+XY=0`. |
|