The number of normals that can be drawn through the point $(2,0)$ to the parabola $y^2=7 x$ is

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(1,4)$ to the parabola $y^2=11 x$, then $2\left(m_1^2+m_2^2\right)=$

If the perpendicular distance from the focus of an ellipse $\frac{x^2}{9}+\frac{y^2}{b^2}=1(b<3)$ to its corresponding directrix is $\frac{4}{\sqrt{5}}$, then the slope of the tangent to this ellipse drawn at $\left(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)$ is

The length of the chord of the ellipse $\frac{x^2}{4}+y^2=1$ formed on the line $y=x+1$ is