The number of integral values of p in the domain [-5,5] , such that the equation 2 x^2+4 x y- p y^2+4 x+ q y+1=0 represents pair of lines, are

Step-by-step solution

Given equation of pair of lines is 2 x^2+4 x y-p y^2+4 x+q y+1=0 Comparing with a x^2+2 ~h x y+ b y^2+2 ~g x+2 f y+ c =0 , we get a =2, ~h =2, ~b =- p If the given equation represents a pair of straight lines, then aligned & h ^2 ab & 4 -2 p & 2 - p & p -2 aligned Possible values of p from domain [-5,5] are -2,-1,0,1,2,3,4,5 . Number of integral values of p=8