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two tangents are drawn from the point (-2,-1) to a parabola. if thita is the angle between them, what is the value of tan thita
Hi Rupali,
You've not mentioned the equation of the parabola. (Assuming it as y^2 = 4x)
The eqn of any tangent to a parabola y^2 = 4ax is y = mx+a/m
So the equation of any tangent to this parabola, would be y=mx+1/m (as a=1, for y^2=4x)
Now these tangents pass through (-2,-1)... so -1=-2m+1/m
Or 2m2-m-1=0.
Where m1,m2 are the slopes of the two tangents that satisfy this equation (m1,m2 are the roots of the quad)....
So tan(angle between the tangents) = |(m1-m2)/(1+m1m2)|
Now m1m2 = -1/2
And m1-m2 = root { (m1+m2)2-4m1m2 } = root [ (1/2)2 - 4(-1/2) ] = root[9/4].
So |m1-m2| = 3/2.
Hence tan(Angle) = (3/2) / (1/2) = 3.....
And that is the answer.
Best Regards,
Ashwin (IIT Madras).
You have to give the equation of parabola.
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