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Lists I, II and III contains conics, equ...

Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively.

If the tangent to a suitable conic (List I) at `(sqrt3(1)/(2))` is found to be `sqrt3x+2y=4`. then which of the following options is the only CORRECT combination?

A

(II) (iii) (R)

B

(IV) (iv) (S)

C

(IV) (iii) (S)

D

(II) (iv) (R)

Text Solution

Verified by Experts

The correct Answer is:
D
Tangent is `(sqrt3,(1)/(2))` is
`sqrt3x+2y=4`
Since slope of tangent at `(sqrt3,(1)/(2))` is `-ve`, possible curves are (I) and (II) only (draw the diagram and verify).
Also, given equation of tangent cannot match with
`my=x^(2)x+a`.
So, comparing eq. (I) with `y=mx+asqrt(x^(2)+1)`, we get
`a=2` and `m=(-sqrt3)/(2)`.
Therefore, equation of curve is `(x^(2))/(4)+y=1`.
The corresponding point of contact is
`((-a^(2)m)/(sqrt(a^(2)m^(2)+1)),(1)/(sqrt(a^(2)m^(2)+1)))`
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