Question

Transforming to parallel axes through a point $(p, q)$, the equation $2x^2 + 3xy + 4y^2 + x + 18y + 25 = 0$ becomes $2x^2 + 3xy + 4y^2 = 1$. Then

• A. $p = -2, q = 3$
• B. $p = 2, q = - 3$
• C. $p = 3, q = - 4$
• D. $p = - 4, q = 3$

Answer 1

Answer: (B)

$p = 2, q = - 3$

Answer 2

The correct answer is B:$p=2,q=-3$
Given that;
$2x^2+3xy+4y^2+x+18y+25=0-(i)$
$2x^2+3xy+4y^2=1-(ii)$
According to the question these two are the equation after transforming to parallel axis(p,q);
i.e., (p,q) satisfies both the equations;
Now;Differentiate equation (i) and ‘x’, then we get;
$4x+3y+1=0-(iii)$
Similarly differentiating equation (ii) w.r.t ‘y’ we get;
$4x+8y=48-(iv)$
So, substituting (p,q) in equation (iii) and (iv) we get;
$\therefore 4p+3q=-1$
$3p+8q=-18$
On solving the above equation we get;
$p=2$ and $q=-3$