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Question

The portion of a tangent to a parabola cut off between the directrix and the curve subtends right angle at the focus.


A

True

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B

False

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Solution

The correct option is A

True


Here we are required to find the angle betwwen PS and DS.

D is the point where the tangent at P meets the directrix.

We know that the equation of the tangent,

ty=x+at2

The tangent passes through a point D(-a,y') situated on the directrix

ty=a+at2

y=a.(t21)t

D(a,a(t21)t)

Slope of SD=a(t21)t(2a)=t212t=m1

Slope of PS=2ata(t21)=2tt21=m2

m1×m2=1

The time segment PD extends right angle at the focus S.


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