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Question

The lines joining the origin to the point of intersection of 3x2+λxy4x+1=0 and 2x+y1=0 are at right angles for

A
λ=4
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B
λ=4
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C
λ=7
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D
no value of λ
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Solution

The correct options are
A λ=4
B λ=4
C λ=7
3x2+λxy4x+1=0

3x2+λxy4x(1)+(1)2=0

2x+y1=0

3x2+λxy4x(2x+y)+(2x+y)2=0

3x2+λxy8x2+4xy+4x2+y2+4xy=0

x2+xy(m+4)+y2=0

x2xy(m+4)y2=0

tanα=2b2aba+b

a=1;b=1

tanα=2111+1

tanα=

=tanα

α=tan1()=90o

λ can be any value from the options
λ=4;λ=4;λ=7.

1464704_196868_ans_c7460305350946ae8dd6d0630f98c51a.jpg

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