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a tangent is drawn from pt.(1,4) to parabola y^2=4ax.find the angle between the tangent and parabola.

a tangent is drawn from pt.(1,4) to parabola y^2=4ax.find the angle between the tangent and parabola.

Grade:12

1 Answers

Nirmal Singh.
askIITians Faculty 44 Points
7 years ago
y^2-2x^3-4y+8=0

Differentiating w.r. x,we get
2ydy/dx-6x^2-4dy/dx=0

dy/dx(2y-4)=6x^2

dy/dx=3x^2/(y-2)

(dy/dx)(1,2)=3/0=infinite

i.e. tangent is perpendiculat to x axis.

so eq. of the tangent is x=k
it passes through (1,2) so

1=k
so eq of tangent will be x=1

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