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From a point (sintheta,costheta), if thr...

From a point `(sintheta,costheta),` if three normals can be drawn tot he parobala `y^2=4a x ,` then the value of `a` is `(1/2,1)` (b) `[-1/2,0]` `[1/2,1]` (d) `(-1/2,0)uu(0,1/2)`

A

(1/2,1)

B

[-1/2,0)

C

[1/2,1]

D

`(-1/2,0cup(0,12))`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Point `(sintheta,costheta)` lies on the circle `x^(2)+y^(2)=1" for "AAthetainR`.
Now, three normals can be drawn to the parabola `y^(2)=4ax` if `x=|2a|` meets this circle.
Hence, we must have
`costhetagt|2a|`
`or0lt|2a|lt1`
`or0|a|lt(1)/(2)`
`orain(-(1)/(2),0)cup(0,(1)/(2))`
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