The values of $\lambda$,for which the point $(\lambda, \lambda-2)$ lies inside the ellipse $4x^2+9y^2=36$ and outside the parabola $y^2=x$,satisfy:

For the hyperbola $\frac{x^2}{9} - \frac{y^2}{3} = 1$,the incorrect statement is:

If the tangent at the point $(1,2)$ on the ellipse $3x^2+4y^2=19$ is also a tangent to the parabola $y^2-kx=0$,then $k=$

If the curves $\frac{x^2}{\alpha} + \frac{y^2}{4} = 1$ and $y^3 = 16x$ intersect at right angles,then a value of $\alpha$ is

Let $P(x_1, y_1)$ and $Q(x_2, y_2)$,with $y_1 < 0$ and $y_2 < 0$,be the endpoints of the latus rectum of the ellipse $x^2 + 4y^2 = 4$. The equations of the parabolas with latus rectum $PQ$ are:
$(A) x^2 + 2\sqrt{3}y = 3 + \sqrt{3}$
$(B) x^2 - 2\sqrt{3}y = 3 + \sqrt{3}$
$(C) x^2 + 2\sqrt{3}y = 3 - \sqrt{3}$
$(D) x^2 - 2\sqrt{3}y = 3 - \sqrt{3}$

If the curves $\frac{x^2}{4}+\frac{y^2}{9}=1$ and $\frac{x^2}{16}-\frac{y^2}{k}=1$ cut each other orthogonally, then $k=$