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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

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

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2 Answers

Ashwin Muralidharan IIT Madras
290 Points
11 years ago

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).

Jaskaran Singh
15 Points
11 years ago

You have to give the equation of parabola.

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