Straight Line Question 217

Question: The equation $ 8x^{2}+8xy+2y^{2}+26x+13y+15=0 $ represents a pair of straight lines. The distance between them is

Options:

A) $ 7/\sqrt{5} $

B) $ 7/2\sqrt{5} $

C) $ \sqrt{7}/5 $

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • [b] The distance between the parallel straight lines given by $ ax^{2}+2hxy+by^{2}+2gx+2fy+c=0 $ is $ 2\sqrt{\frac{g^{2}-ac}{a(a+b)}} $ Here, $ a=8,b=2,c=15,g=13 $ So, req. distance $ =2\sqrt{\frac{169-120}{80}}=2\times \frac{7}{4\sqrt{5}}=\frac{7\sqrt{5}}{10} $

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