Question

In order to make the first degree terms missing in the equation $2x^2+7y^2+8x-14y+15=0$, the origin should be shifted to the point

• A. $(1,-2)$
• B. $(-2,-1)$
• C. $(2,1)$
• D. $(-2,1)$

Answer 1

The correct option is D $(-2,1)$

Given, $2x^2+7y^2+8x-14y+15=0$

$2x^2+8x+7y^2-14y+15=0$

$2(x^2+4x)+7(y^2-2y)+15=0$

$2\left(\right(x+2{)}^2-4)+7((y-1{)}^2-1)+15=0$

$2(x+2{)}^2-8+7(y-1{)}^2-7+15=0$

$2(x+2{)}^2+7(y-1{)}^2=0$

Therefore for no first degree terms,

$x+2=0$, $x=-2$ and $y-1=0$

$y=1$.

Thus the origin needs to be shifed to

$(-2,1)$.