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 $$PAB$$.