If the ellipse `x^2/4+y^2/1=1` meets the ellipse `x^2/1+y^2/a^2=1` in four distinct points and `a=b^2-10b+25`,then the number of integral values which are not in range of `b` is

If the ellipse (x^2)/4+y^2=1 meets the ellipse x^2+(y^2)/(a^2)=1 at four distinct points and a=b^2-5b+7, then b does not lie in [4,5] (b) (-oo,2)uu(3,oo) (-oo,0) (d) [2,3]

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

A tangent to the hyperbola x^(2)/4 - y^(2)/1 = 1 meets ellipse x^(2) + 4y^(2) = 4 in two distinct points . Then the locus of midpoint of this chord is

A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1 and to cut the ellipse x^2/c^2+y^2/d^2=1 at the points P and Q. If the tangents are at right angles, then the value of (a^2/c^2)+(b^2/d^2) is

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 x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

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

If the line y=x+sqrt(3) touches the ellipse (x^(2))/(4)+(y^(2))/(1)=1 then the point of contact is

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(b^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is