If one of the lines in the pair of straight line given by 4 x^2+6 x y+k y^2=0 bisects the angle between the coordinate axes, then k

Step-by-step solution

Since, one of the lines represented by a x^2+2 h x y+k y^2=0 bisect the angle between the axes therefore its equation is y=x . Since, y=x satisfies a x^2+2 h x y+b y^2=0 , therefore a x^2+2 h x^2+b x^2=0 Now for equation 4 x^2+6 x y+k y^2=0 Here, a=4, h=3, b=k Now from Eq. (i) array rlrl & & (4+k)^2 & =4(3)^2=36 & & 4+k & = 6 & k & =2,-10 array Hence, k -10,2