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) m y = m 2 x + a (P) a m 2 , 2 a m (II) x 2 + a 2 y 2 = a 2 (ii) y = m x + a   m 2 + 1 (Q) - m a m 2 + 1 , a m 2 + 1 (III) y 2 = 4 a x…

Question

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) $m y = m^{2} x + a$	(P) $(\frac{a}{m^{2}}, \frac{2 a}{m})$
(II) $x^{2} + a^{2} y^{2} = a^{2}$	(ii) $y = m x + a \sqrt{m^{2} + 1}$	(Q) $(\frac{- m a}{\sqrt{m^{2} + 1}}, \frac{a}{\sqrt{m^{2} + 1}})$
(III) $y^{2} = 4 a x$	(iii) $y = m x + \sqrt{a^{2} m^{2} - 1}$	(R) $(\frac{- a^{2} m}{\sqrt{a^{2} m^{2} + 1}}, \frac{1}{\sqrt{a^{2} m^{2} + 1}})$
(IV) $x^{2} - a^{2} y^{2} = a^{2}$	(iv) $y = m x + \sqrt{a^{2} m^{2} + 1}$	(S) $(\frac{- a^{2} m}{\sqrt{a^{2} m^{2} - 1}}, \frac{- 1}{\sqrt{a^{2} m^{2} - 1}})$

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 Correct combination for obtaining its equation?

Aicharya · Accepted Answer

For a = &#160; 2 and point ( - 1 , &#160; 1 ) only I of column-1 satisfies. Hence, equation of tangent is - x + y = 2 or y = x + 2 &#160; &#160; &#8658; &#160; &#160; m = 1 which matches with (ii) of column 2 and also with Q of column 3

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

Solution