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

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?

TestHub · Accepted Answer

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

Mathematics - Ellipse Question with Solution | TestHub

Options:

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