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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.
Column-1
Column-2
\( \mathrm{P} \)
(I) \( x^{2}+y^{2}=a^{2} \)
(i) \( m y=m^{2} x+a \)
\( (P)\left(\frac{a}{m^{2}}, \frac{2 a}{m}\right) \)
W
(II) \( x^{2}+a^{2} y^{2}=a^{2} \)
(ii) \( y=m x+a \sqrt{m^{2}+1} \)
(Q) \( \left(\frac{-m a}{\sqrt{m^{2}+1}}, \frac{a}{\sqrt{m^{2}+1}}\right) \)
(III) \( y^{2}=4 a x \quad \) (iii) \( y=m x+\sqrt{a^{2} m^{2}-1} \)
(R) \( \left(\frac{-a^{2} m}{\sqrt{a^{2} m^{2}+1}}, \frac{1}{\sqrt{a^{2} m^{2}+1}}\right) \)
(IV) \( x^{2}-a^{2} y^{2}=a^{2} \)
(iv) \( y=m x+\sqrt{a^{2} m^{2}+1} \)
(S) \( \left(\frac{-a^{2} m}{\sqrt{a^{2} m^{2}-1}}, \frac{-1}{\sqrt{a^{2} m^{2}-1}}\right) \)
For \( a=\sqrt{2} \), if a tangent is drawn to a suitable conic
(Column 1) at the point of contact \( (-1,1) \), then which of the following options is the only CORRET combination \( \rightarrow \) for obtaining its equation ?
(a) (I) (ii) (Q)
(b) (I) (i) (P)
(c) (III) (i) (P)
(d) (II) (ii) (Q)
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