If the equation `2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0` represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

Options

A. 2
B. 4
C. `sqrt7`
D. 0

Answer

B

Explanation

The x-coordinates of the points of intersection of the pair of lines by `2x^(2)+2hxy+6y^(2)-4x+5y-6=0` and x-axis are roots of the equation
`2x^(2)-4x-6=0`
or, `x^(2)-2x-3=0`
`rArr" "(x-3)(x+1)=0 rArr x=-1, 3`
Hence, required length `=|x_(1)-x_(2)|=4.`