1.

Consider the equation of a pair of straight lines as lambdax^(2)-10xy+12y^(2)+5x-16y-3=0.The point of intersection of lines is (alpha, beta). Then the value of alpha beta is

Answer»

35
45
20
15

Solution :`2x^(2)=10xy+12y^(2)+5x-16y-3=0`
Consider the HOMOGENEOUS PART
`2x^(2)-10xy+12y^(2)=(x-2y)(2x-6)`
`2x^(2)-10xy+12y^(2)+5x-16y-3`
`-=(2x-6y+A)(x-2y+B)`
Comparing coefficients , we get
`A=-1,B=3`
Hence , the lines are
`2x-6y-1=0and x-2y+3=0`Solving , we get the intersection points as`(-10,-7//2)`. THEREFORE , Product `=35`


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