Let `u=a x+b y+a ^3sqrt(b)=0,v=b x-a y+b^3sqrt(a)=0,a ,b in R ,` be two straight lines. The equations of the bisectors of the angle formed by `k_1u-k_2v=0` and `k_1u+k_2v=0` , for nonzero and real `k_1` and `k_2` are

If x=(3)/(k) be the equation of directrix of the parabola y ^(2) + 4 y + 4 x + 2 = 0 then , k is _

If k x^2 + 10 xy + 3 y^2 - 15x - 21y + 18 = 0 represents a pair of straight lines. Then the value of k is :

If x = 2k + 1 and y = k is a solutions of the equation 5x + 3y - 7 = 0, find the value of k.

The set of real values of k for which the lines x + 3y +1=0, kx + 2y-2=0 and 2x-y + 3 = 0 form a triangle is

Determine the mass of each element in (a) 2.0 moles of K (b) 0.1 mole of U

Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are y=+-x Statement - II : Equation of the bisectors of the angles between the lines a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0 are (a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2))) (Provided a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)

If the distance between the lines 5x+12y-1=0and10x+24y+k=0 be 2 units then the value of k is -

If the equation |x^2+b x+c|=k has four real roots, then a. b^2-4c > 0 and 0 0 and k > (4c-b^2)/4 d. none of these

The asymptotes of the hyperbola x y=h x+k y are (1) x-k=0 and y-h=0 (2)x+h=0 and y+k=0 (3) x-k=0 and y+h=0 (4)x+k=0 and y-h=0

The real number k of for which the equation 2x^3+3x+k=0 has two distinct real roots in [0,1]