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 if

The point (t^(2)+2t+5,2t^(2)+t-2) lies on the line x+y=2 for

If the normals at points t_(1) and t_(2) meet on the parabola,then t_(1)t_(2)=1 (b) t_(2)=-t_(1)-(2)/(t_(1))t_(1)t_(2)=2( d) none of these

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

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