Question

The equation of the perpendiculars drawn from the origin to the lines represented by the equation

$2x^{2} - 10xy + 12y^{2} + 5x - 16y - 3 = 0$ is

• A. $6x^{2} + 5xy + y^{2} = 0$
• B. $6y^{2} + 5xy + x^{2} = 0$
• C. $6x^{2} - 5xy + y^{2} = 0$
• D. None of these

Answer 1

Answer: (A)

$6x^{2} + 5xy + y^{2} = 0$

Answer 2

We know that the equation of perpendicular drawn from origin on $ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0$

is $bx^{2} - 2hxy + ay^{2} = 0$.

Therefore, the required equation is given by

$12x^{2} + 10xy + 2y^{2} = 0$or $6x^{2} + 5xy + y^{2} = 0$.