If a number of ellipses whose major axis is x -axis and the minor...

Since the minor axis is variable, hence& $e$ is a variable quantity

Therefore the equation of the tangent to the ellipse can be written as $\dfrac{xae}{a^{2}} + \dfrac{yb^{2}}{ab^{2}} = 1$
$⇒ ex + y = a ⇒ y - a + ex = 0$
This line passes through the fixed point~$\left(0, a\right)$ (where $a = 1$)

Hence, distance fro the centre of the ellipse~$= 1$