Give the answer Q.8, Q.9 and Q.10 by appropriately matching the information given in the three columns of the following table.
Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, repectively.
PW
\[
\begin{array}{l}
\text { (I) } x^{2}+y^{2}=a^{2} \quad(\text { i }) m y=m^{2} x+a \quad(P)\left(\frac{a}{m^{2}}, \frac{2 a}{m}\right) \\
\text { (III) } y^{2}=4 a x \quad \text { (iii) } y=m x+\sqrt{a^{2} m^{2}-1} \quad(R)\left(\frac{-a^{2} m}{\sqrt{a^{2} m^{2}+1}}, \frac{1}{\sqrt{a^{2} m^{2}+1}}\right) \\
\text { (IV) } x^{2}-a^{2} y^{2}=a^{2} \quad \text { (iv) } y=m x+\sqrt{a^{2} m^{2}+1} \quad(S)\left(\frac{-a^{2} m}{\sqrt{a^{2} m^{2}-1}}, \frac{-1}{\sqrt{a^{2} m^{2}-1}}\right) \\
\end{array}
\]
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?
\( (a)(\mathrm{II})(\mathrm{i})(\mathrm{P}) \)
(b) (I) (ii) \( (\mathrm{Q}) \)
(c) (II) (iv) (R)
(d) (III) (ii) (Q)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
0