The line `x=t^2` meets the ellipse `x^2+(y^2)/9=1` at real and distinct points if and only if. `|t|<2` (b) `|t|<1` `|t|>1` (d) none of these

The line y=2t^2 meets the ellipse (x^2)/(9)+(y^2)/(4)=1 in real points if

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

If the normals at points t_1 and t_2 meet on the parabola, then (a) t_1t_2=1 (b) t_2=-t_1-2/(t_1) (c) t_1t_2=2 (d) none of these

From any point on the line (t+2)(x+y) =1, t ne -2 , tangents are drawn to the ellipse 4x^(2)+16y^(2) = 1 . It is given that chord of contact passes through a fixed point. Then the number of integral values of 't' for which the fixed point always lies inside the ellipse is

Write the equation of a tangent to the curve x=t, y=t^2 and z=t^3 at its point M(1, 1, 1): (t=1) .

The locus of the represented by x = t^ 2 + t + 1 , y = t ^ 2 - t + 1 is

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

The differential coefficient of sin^(-1)t/(sqrt(1+t^2))w.r.t cos^(-1)1/(sqrt(1+t^2)) is (a) 1 AAt >0 (b) -1AAt<0 (c) 1AAt in R (d) None of these

The eccentricity of the conic x=3((1-t^(2))/(1+t^(2))) and y=(2t)/(1+t^(2)) is

For the curve x=t^(2) +3t -8 ,y=2t^(2)-2t -5 at point (2,-1)