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The lines joining the origin to the point of intersection of 3x^2+lambda xy -4x+1=0 and 2x+y-1=0 are at right angles for Lambda= A.-4, B.4 , C.7 D.No value of lamda

The lines joining the origin to the point of intersection of 3x^2+lambda xy -4x+1=0 and 2x+y-1=0 are at right angles for
Lambda= A.-4, B.4 , C.7 D.No value of lamda 

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
3 years ago
Here we have to use the concept of homoginization

2x + y =1 is the given line.

3x^2+\lambda xy -4x(2x + y)+1(2x + y)^2=0
3x^2+\lambda xy -8x^2 - 4xy + 4x^2 + y^2 + 4xy = 0
Now apply a + b = 0 as agle is 90 deg

3x^2+\lambda xy -8x^2 - 4xy + 4x^2 + y^2 + 4xy = 0
-x^2+\lambda xy + y^2= 0

So answer should be all values of lambda

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