Question

The product of perpendiculars drawn from the point $(1,2)$ to the pair of lines $x^2+4xy+y^2=0$

• A. $\frac{13}{4}$
• B. $\frac{3}{4}$
• C. $\frac{9}{16}$
• D. none of these

Answer 1

Answer: (A)

$\frac{13}{4}$

The product of the perpendicular drawn from the point $(x_1,y_1)$ on the lines $a{x}^2+2hxy+b{y}^2=0$ is

$\left|\frac{a{x}_1^2+2h{x}_1{y}_1+b{y}_1^2}{\sqrt{{(a-b)}^2+4h^2}}\right|$

For line $x^2+4xy+y^2=0$ from point $(1,2)$ is

$\left|\frac{1{.1}^2+2.2.1.2+1.2^2}{\sqrt{{(1-1)}^2+4.2^2}}\right|=\frac{13}{4}$