Pair Of Straight Lines Question 35

Question: The product of perpendiculars drawn from the origin to the lines represented by the equation $ ax^{2}+2hxy+by^{2}+2gx+2fy+c=0 $ , will be

[Bihar CEE 1994]

Options:

A) $ \frac{ab}{\sqrt{a^{2}-b^{2}+4h^{2}}} $

B) $ \frac{bc}{\sqrt{a^{2}-b^{2}+4h^{2}}} $

C) $ \frac{ca}{\sqrt{(a^{2}+b^{2})+4h^{2}}} $

D) $ \frac{c}{\sqrt{{{(a-b)}^{2}}+4h^{2}}} $

Show Answer

Answer:

Correct Answer: D

Solution:

The product of perpendiculars $ =\frac{c}{\sqrt{{{(a-b)}^{2}}+4h^{2}}} $ .