Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) If BC is latus rectum of parabola `y^2` = 4ax and A is the vertex. Then the minimum legnth of the projection of BC on a tangent drawn in the portion BAC is - Sarthaks eConnect

If BC is latus rectum of parabola `y^2` = 4ax and A is the vertex. Then the minimum legnth of the projection of BC on a tangent drawn in the portion BAC is :

If BC is latus rectum of parabola `y^2` = 4ax and A is the vertex. Then the minimum legnth of the projection of BC on a tangent drawn in the portion BAC is :

A.

`sqrt2a`

B.

`2sqrt2a`

C.

2a

D.

`root 3 2a`

Solution

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Best answer

Let tangent at `P(at^2 , 2at)` make an angle `theta`with x-axis, then `tantheta` = `1/t.` Projection of BC on tangent

BC Sin `theta` = `(4a)/sqrt(1+t^2) 2asqrt2 (as - <=t<=1)`