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Question

What is the condition for a conic x2+2xy+2y+kx+3y2=0 to represent a pair of straight lines.



A

k=1

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B

k=12

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C

k=2

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D

k=12

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Solution

The correct option is C

k=2


This is a straight forward condition. For a conic of the general form,

ax2+2hxy+2gx+2fy+by2+c=0 to represent a pair of straight line, the required condition in determinant form is,

∣ ∣ahghbfgfc∣ ∣=0

The given conic equation is,

x2+2xy+2y+kx+3y2=0

Where,

a=1,b=1,h=1,g=k2,f=1,c=0;

Putting these values in the condition we get,

∣ ∣ ∣11k2111k211∣ ∣ ∣=0

∣ ∣ ∣11k21111k211∣ ∣ ∣=0

(k21)(1k2)=0

k2=1k=2,
Which is the required condition.


Mathematics

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