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If the length of a focal chord of the pa...

If the length of a focal chord of the parabola `y^2=4a x` at `a` distance `b` from the vertex is `c ,` then prove that `b^2c=4a^3dot`

Text Solution

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In the figure, OM = b = distance of focal chord PQ make an angle `theta` with positive x-axis.
`:." "PQ=4acosec^(2)theta`
Now, in right angled triangle OMS,
`sintheta=OM//OS=b//a`
`:." "PQ=4a(a//b)^(2)=4a^(3)//b^(2)`
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