First slide

Pair of straight lines

Question

The product of the perpendicular from origin to the pair of lines $5 x^{2} + 12 xy + 6 y^{2} + x + y - 7 = 0$ is

Moderate

A

$- \frac{7}{\sqrt{145}}$
B

$\frac{7}{\sqrt{145}}$
C

$\frac{\sqrt{145}}{7}$
D

$- \frac{\sqrt{145}}{7}$

Solution

The product of the perpendiculars drawn from the point $P (0, 0)$ to the pair of lines represented by the equation ${ax}^{2} + 2 hxy + {by}^{2} + 2 gx + 2 fy + c = 0 is |\frac{c}{\sqrt{{(a - b)}^{2} + 4 h^{2}}}|$
For the equation $5 x^{2} + 12 xy + 6 y^{2} + x + y - 7 = 0$ the product of the perpendiculars from the point $(0, 0)$ is d
$\begin{array}{l} d = |\frac{- 7}{\sqrt{{(5 - 6)}^{2} + {(12)}^{2}}}| \\ = |\frac{7}{\sqrt{145}}| \end{array}$
Therefore, the required distance is $\frac{7}{\sqrt{145}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App