If sum of the slopes of the lines given by `x^(2)-pxy+8y^(2)=0` is three times their product then p= . . .

Options

A. `(3)/(4)`
B. `(1)/(4)`
C. `4`
D. 3

Answer

A

Explanation

Given, pair of lines, `x^(2)-4pxy+8y^(2)=0`
which is in the form of `ax^(2)+2hxy+by^(2)=0`
Accordingg to question,
Sum of the slopes `=3xx`product of the slopes
`impliesm_(1)+m_(2)=3xx(m_(1)m_(2))`
`implies(-(-4p))/(8)=3xx(1)/(8)`
`implies4p=3impliesp=(3)/(4)`