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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? |
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Answer» (II) (iii) (R) `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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