The line `x=t` 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

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 (a) [4,5] (b) (-oo,2)uu(3,oo) (c) (-oo,0) (d) [2,3]

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

Let Sa n dS ' be two foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If a circle described on S S^(prime) as diameter intersects the ellipse at real and distinct points, then the eccentricity e of the ellipse satisfies (a) c=1/(sqrt(2)) (b) e in (1/(sqrt(2)),1) (c) e in (0,1/(sqrt(2))) (d) none of these

The straight line (x)/(4)+(y)/(3) =1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9) =1 at two points A and B, there is a point P on this ellipse such that the area of DeltaPAB is equal to 6(sqrt(2)-1) . Then the number of such points (P) is/are

The line y = 2x + c touches the ellipse (x^2)/(16) + (y^2)/(4) = 1 if c is equal to

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then -1 1 m in R (d) none of these

P is the point on the ellipse is x^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

P is the point on the ellipse is x^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

The slopes of the common tanents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are (a) +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

If a ,b ,c are three distinct positive real numbers, the number of real and distinct roots of a |x^2|+2b|x|-c=0 is a. 0 b. 4 c. 2 d. none of these