The equation of straight line passing through `(-a ,0)` and making a triangle with the axes of area `T` is (a) `2T x+a^2y+2a T=0` (b)`2T x-a^2y+2a T=0` (c)`2T x-a^2y-2a T=0` (d)none of these

The equation of straight line passing through (-a,0) and making a triangle with the axes of area T is (a) 2Tx+a^(2)y+2aT=0 (b) 2Tx-a^(2)y+2aT=0( c) 2Tx-a^(2)y-2aT=0 (d)none of these

Find the equation of the straight lines passing through the following pair of point: (0,-a)a n d\ (a t_2,\ a//t_2)

Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the x-axis at point B and D , respectively. If the rectangle A B C D is completed, then the locus of C is (a)y=2a (b) y+2a=c (c)x=2a (d) none of these

Locus of the middle points of the line segment joining P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t) cuts an intercept of length a on the line x+y=1 , then a = (A) 1/sqrt(2) (B) sqrt(2) (C) 2 (D) none of these

Locus of the middle points of the line segment joining P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t) cuts an intercept of length a on the line x+y=1 , then a = (A) 1/sqrt(2) (B) sqrt(2) (C) 2 (D) none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

The parametric equations of a parabola are x=t^2+1, y=2t+1. The Cartesian equation of its directrix is a. x=0 b. x+1=0 c. y=0 d. none of these

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) non of these

The equation of the tangent to the curve x = (t - 1)/(t + 1), y = (t + 1)/(t - 1) at t = 2 is a) x + 9y - 6 = 0 b) 9x - y - 6 = 0 c) 9x + y + 6 = 0 d) 9x + y - 6 = 0