### Ellipse

goals
The maximum number of normals that can be drawn from any point to the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ are
Find $b$ if $\dfrac{x^2}{16}+\dfrac{y^2}{b^2}=8$ passes through $(8,10)$
The minimum distance of the center of the ellipse $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1$ from the chord of contact of manually perpendicular tangents of the ellipse is ?
If $\left(m_i, \dfrac{1}{m_i}\right), i=1, 2, 3, 4$ are concyclic points then the value of $m_1m_2m_3m_4$ is?
Tangents $PA$ and $PB$ are drawn to $x^{2}+y^{2}=a^{2}$ from the point $P(x_{1} ,y_{1})$. Then find the equation of the circumcircle of triangle $PAB$.