If a circle passing through $A(1,1)$ touches the $X$-axis, then the locus of the other end of the diameter through $A$ is

If two circles $x^2+y^2-6 x-6 y+13=0$ and $x^2+y^2-8 y+9=0$ intersect at $A$ and $B$, then the focus of the parabola whose directrix is the line $A B$ and vertex is the point $s(a, b)$ is

A particle is travelling in clockwise direction on the ellipse $\frac{x^2}{100}+\frac{y^2}{25}=1$. If the particle leaves the ellipse the point $(-8,3)$ on it and travels along the tangent to the ellipse at that point, then the point where the particle crosses the $Y$-axis is

If the equation of a hyperbola is $9 x^2-16 y^2+72 x-32 y-16=0$, then the equation of conjugate hyperbola is