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Question

Columns 1,2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.
​​​​​​Column1Column2Column3(I)x2+y2=a2(i)my=m2x+a(P)(am2,2am)(II)x2+a2y2=a2(ii)y=mx+am2+1(Q)(mam2+1,am2+1)(III)y2=4ax(iii)y=mx+a2m21(R)(a2ma2m2+1,1a2m2+1)(IV)x2a2y2=a2(iv)y=mx+a2m2+1(S)(a2ma2m21,1a2m21)

For a=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?

A
(I)(i)(P)
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B
(I)(ii)(Q)
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C
(II)(ii)(Q)
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D
(III)(i)(P)
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Solution

The correct option is B (I)(ii)(Q)
The correct combination of curve, tangent and point of contact is given in the table below:
(I)(ii)(Q)(II)(iv)(R)(III)(i)(P)(IV)(iii)(S)

a=2 and point (1,1) satisfies curve x2+y2=a2,
equation of tangent is y=mx+am2+1 and point of contact is (mam2+1,am2+1)

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