Question

The point to which the origin should be translated in order to male the first degree terms missing in the equation 3xy - 2x + y - 8 = 0 is​

Answer 1

Refer the picture....

We have taken 3k - 2 and 3h + 1 equal to 0 as it is given in the question that first degree terms miss, that is, the coefficients of X and Y should be 0...

Answer 2

Given:

3xy - 2x + y - 8 = 0  -> original

(h , k)   (x , y)->old   (x , y)->new

x = x + h y = y + k

$\begin{array}{l}3(x+h)(y+k)-2(x+h)+y+k-8=0 \\(3 x+3 h)(y+k)-2 x-2 h+y+k-8=0\end{array}$

$3 x y+3 x k+3 h y+3 h k-2 x+y-2 h+k-8=0$

$3 x y+x(3 k-2)+y(3 h+1)+3 k h-2 h+k-8=0$

$\begin{aligned}3 k-2 &=0 \Rightarrow k=2 / 3 \\3 h+1 &=0 \Rightarrow h=-1 / 3\end{aligned}$

hence the answer is (h , k)= (2/3 , -1/3)