Question

Equation of a line which is parallel to the line common to the pair of lines given by $6x^2-xy-12y^2-0$ and $15x^2+14xy-8y^2-0$ and at a distance 7 from it is

• A. $3x+4y=35$
• B. $5x-2y=7$
• C. $3x+4y=-35$
• D. $2x-3y=7$

Answer 1

Answer: (A), (C)

The correct options are
A

$3x+4y=35$

C

$3x+4y=-35$

$6x^2-xy-12y^2=0$
$\Rightarrow$ (2x - 3y)(3x + 4y) = 0 (i)
and $15x^2$ + 14xy - $8y^2$ = 0
$\Rightarrow$ (5x - 2y) (3x + 4y) = 0 (ii)
Equation of the line common to (i) and (ii) is
3x + 4y = 0 (iii)
Equation of any line parallel to (ii) is
3x + 4y = k
Since its distance from (iii) is 7
$\left|\frac{k}{\sqrt{3^2+4^2}}\right|=7\Rightarrow k=\pm (7\times 5)=\pm 35$