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

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=a(sin t-t cos t),y=a sin t then find the value of (d^(2)y)/(dx^(2))

If x=t^(2) and y=2t then equation of the normal at t=1 is

If the equation 4x^2+2xy+2y^2 - 1=0 becomes 5X^2+Y^2=1 when the axes are rotated through an angle of t degrees then sum of the digits of t is

Which of the following curves in the x -y plane cuts every straight line in the plane? (1) x=t,y=t^(2) and (2)x=t,y=t^(3) and (3) x=t^(2),y=t^(3) and x=t^(3),y=t^(5)

The radius of the circle t^(2) x^(2) + t^(2) y^(2) - 2at^(3) x - 2 aty + a^(2) t^(4) - a^(2) t^(2) + a^(2) = 0 is

The function y=f(x) is defined by x=2t-|t|,y=t^(2)+|t|,t in R in the interval x in[-1,1], then

t_(1),t_(2),t_(3) are lengths of tangents drawn from a point (h,k) to the circles x^(2)+y^(2)=4,x^(2)+y^(2)-4=0andx^(2)+y^(2)-4y=0 respectively further, t_(1)^(4)=t_(2)^(2)" "t_(3)^(2)+16 . Locus of the point (h,k) consist of a straight line L_(1) and a circle C_(1) passing through origin. A circle C_(2) , which is equal to circle C_(1) is drawn touching the line L_(1) and the circle C_(1) externally. Equation of C_(1) is

Equation of normal to x= 2e^(t), y= e^(-t) " at " t=0 is