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  • From the point N(5,2) normals are drawn to the parabola to meet the curve at A and

From the point N(5,2) normals are drawn to the parabola \mathrm{y^2=4 x} to meet the curve at A and B. If the tangents to the curve at A and B meet at the point T, then \mathrm{T N^2} is equal to

Option: 1

50


Option: 2

60


Option: 3

40


Option: 4

70


Answers (1)

best_answer

\mathrm{\text { The normal at } t \text { is } x t+y=t^3+2 t \text {. }}

It passes through N(5, 2).

\mathrm{\therefore t^3-3 t-2=0, \text { Solving } t=-1,-1,2}

\mathrm{\text { The points are given by }\left(t^2, 2 t\right)}

A ≡ (1, –2), B ≡ (4, 4)
The tangents at A and B meet at

\mathrm{T\left(t_1 t_2, t_1+t_2\right) \text { or } T \equiv(-2,1), T N^2=(5+2)^2+(2-1)^2=50 \text {. }}

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Gunjita

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