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

If a normal is drawn at a variable point $P(x, y)$ on the curve $9 x^2+16 y^2-144=0$, then the maximum distance from the centre of the curve to the normal is

A line segment joining a point $A$ on $X$-axis to a point $B$ on $Y$-axis is such that $A B=15$. If $P$ is a point on $A B$ such that $\frac{A P}{P B}=\frac{2}{3}$, then the locus of $P$ is

If any tangent drawn to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ touches one of the circles $x^2+y^2=\alpha^2$, then the range of $\alpha$ is