Columns 1, 2 and 3 contain conics, equations of tangents to the...

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.

Column 1	Column 2	Column 3
(I) ${x}^{2} + {y}^{2} = {a}^{2}$	(i) $my = {m}^{2}x + a$	(P) \left(\dfrac{a}{{m}^{2}}, \dfrac{2a}{m}\right)$</td> </tr> <tr> <td>(II)${x}^{2} + {a}^{2}{y}^{2} = {a}^{2}$</td> <td>(ii)$y = mx + a\sqrt{{m}^{2} + 1}$</td> <td>(Q) \left(\dfrac{- ma}{\sqrt{{m}^{2} + 1}}, \dfrac{a}{\sqrt{{m}^{2} + 1}}\right)$
(III) ${y}^{2} = 4ax$	(iii) $y = mx + \sqrt{{a}^{2}{m}^{2} - 1}$	(R) \left(\dfrac{- {a}^{2}m}{\sqrt{{a}^{2}{m}^{2} + 1}}, \dfrac{1}{\sqrt{{a}^{2}{m}^{2} + 1}}\right)$</td> </tr> <tr> <td>(IV)${x}^{2} - {a}^{2}{y}^{2} = {a}^{2}$</td> <td>(iv)$y = mx + \sqrt{{a}^{2}{m}^{2} + 1}$</td> <td>(S) \left(\dfrac{- {a}^{2}m}{\sqrt{{a}^{2}{m}^{2} - 1}}, \dfrac{- 1}{\sqrt{{a}^{2}{m}^{2} - 1}}\right)$

If a tangent to a suitable conic (Column 1) is found to be $y = x + 8$ and its point of contact is $( 8, 16 )$, then which of the following options is the only Correct combination?