Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, x2+y2=a, (i), my=m2x+a, (P), (m2a,m2a)II, x2+a2y2=a, (ii), y=mx+am2+1, (Q), (m2+1−ma,m2+1a)III, y2=4ax, (iii), y=mx+a2m2−1, (R), (a2m2+1−a2m,a2m2+11)IV, x2−a2y2=a2, (iv), y=mx+a2m2+1, (S), (a2m2+1−a2m,a2m2+1−1)If a tangent to a suitable conic (Column 1) is found to be y=x+8and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)

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Column 1,2 and 3 contains conics, equations of tangents to the

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Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, $x^{2} + y^{2} = a$ , (i), $m y = m^{2} x + a$ , (P), $(\frac{a}{m ^{2}}, \frac{2 a}{m})$ II, $x^{2} + a^{2} y^{2} = a$ , (ii), $y = m x + a m^{2} + 1$ , (Q), $(\frac{- m a}{m ^{2} + 1}, \frac{a}{m ^{2} + 1})$ III, $y^{2} = 4 a x$ , (iii), $y = m x + a^{2} m^{2} - 1$ , (R), $(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{1}{a ^{2} m ^{2} + 1})$ IV, $x^{2} - a^{2} y^{2} = a^{2}$ , (iv), $y = m x + a^{2} m^{2} + 1$ , (S), $(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{- 1}{a ^{2} m ^{2} + 1})$ 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 followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)

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Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I,

x^{2} + y^{2} = a

, (i),

m y = m^{2} x + a

, (P),

(\frac{a}{m ^{2}}, \frac{2 a}{m})

II,

x^{2} + a^{2} y^{2} = a

, (ii),

y = m x + a m^{2} + 1

, (Q),

(\frac{- m a}{m ^{2} + 1}, \frac{a}{m ^{2} + 1})

III,

y^{2} = 4 a x

, (iii),

y = m x + a^{2} m^{2} - 1

, (R),

(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{1}{a ^{2} m ^{2} + 1})

IV,

x^{2} - a^{2} y^{2} = a^{2}

, (iv),

y = m x + a^{2} m^{2} + 1

, (S),

(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{- 1}{a ^{2} m ^{2} + 1})

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 followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)

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Question Text	Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, $x^{2} + y^{2} = a$ , (i), $m y = m^{2} x + a$ , (P), $(\frac{a}{m ^{2}}, \frac{2 a}{m})$ II, $x^{2} + a^{2} y^{2} = a$ , (ii), $y = m x + a m^{2} + 1$ , (Q), $(\frac{- m a}{m ^{2} + 1}, \frac{a}{m ^{2} + 1})$ III, $y^{2} = 4 a x$ , (iii), $y = m x + a^{2} m^{2} - 1$ , (R), $(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{1}{a ^{2} m ^{2} + 1})$ IV, $x^{2} - a^{2} y^{2} = a^{2}$ , (iv), $y = m x + a^{2} m^{2} + 1$ , (S), $(\frac{- a ^{2} m}{a ^{2} m ^{2} + 1}, \frac{- 1}{a ^{2} m ^{2} + 1})$ 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 followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)
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