Match the following and mark the correct options

Options

A. (II) (iii) (R)
B. (IV) (iv) (S)
C. (IV) (iii) (S)
D. (II) (iv) (R)

Answer

D

Explanation

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)))`