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).

Approved

You have to give the equation of parabola.