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Question

The value of p for which the equation x2+pxy+y2-5x-7y+6=0 represents a pair of straight lines, is


A

52

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B

5

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C

2

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D

25

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Solution

The correct option is A

52


Explanation for the correct answer:

Compute the required value:

The given equation is x2+pxy+y2-5x-7y+6=0 ...(i)

The general form of a second-degree equation is given as

ax2+2hxy+by2+2gx+2fy+c=0 ...(ii)

Comparing equations i and ii we get

a=1,h=p2,b=1,g=-52,f=-72,c=6

The condition for a general second-degree equation to be a pair of straight lines is

abc+2fgh−af2−bg2−ch2=0

Substituting all the required values we get,

6+2×-72×-52×p2--722--522-6p22=0

⇒ 6+35p4-494-254-6p24=0

⇒ 24+35p-74-6p2=0

⇒ 6p2+35p-50=0

⇒ (2p−5)(3p−10)=0

⇒ p=52 or p=103

Hence from the given options the value of p is 52.

Hence, option A is the correct answer.


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