Let L be a tangent line to the parabola y ^ 2 = 4x - 20 at (6, 2) ....

The equation of a tangent to a parabola ${y}^{2} = 4a\left(x - h\right)$ at a point \left({x}_{1}, {y}_{1}\right)$on it is$y{y}_{1} = 4a\left(\left(\dfrac{x + {x}_{1}}{2}\right) - h\right) .$</p><p>Hence, the equation of tangent to parabola${y}^{2} = 4x - 20$at \left(6, 2\right)$ is $2y = 2 ( x + 6 ) - 20$

$⇒ y = x - 4 .$

Also, a line $y = mx + c$ is a tangent to the ellipse $\dfrac{{x}^{2}}{{a}^{2}} + \dfrac{{y}^{2}}{{b}^{2}} = 1$ if ${c}^{2} = {a}^{2}{m}^{2} + {b}^{2} .$

Hence, by using the condition of tangency for ellipse$\dfrac{{x}^{2}}{2} + \dfrac{{y}^{2}}{b} = 1 and the line$y = x - 4,$we get</p><p>$16 = 2 ( 1{)}^{2} + b$</p><p>$⇒ b = 14 .$