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Consider the equation of a pair of strai...

Consider the equation of a pair of straight lines as `2x^(2)-10xy+12y^(2)+5x-16y-3=0`. The point of intersection of lines is `(alpha, beta)`. Then the value of `alpha beta` is (a) 35 (b) 45 (c) 20 (d) 15

A

35

B

45

C

20

D

15

Text Solution

Verified by Experts

The correct Answer is:
1
`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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