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angle between tangents drawn from origin to parabola y 2 =4a(x-a) is ?

angle between tangents drawn from origin to parabola y2=4a(x-a) is ?

Grade:11

1 Answers

Trina
34 Points
5 years ago
let the equation of the tangent y=mx (since c=0)
putting y=mx in the eqn of parabola
m^2x^2=4a(x-a)
m^2x^2-4ax+4a^2=0
D=0 (since the tangent cuts the parabola at 1 pt...roots are equal)
(4a)^2=4(4a^2)m^2
m=+1 or m=-1
we get the slopes of the 2 tangents as +1 and -1
product of slopes =-1
therefore angle between them is 90
 

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