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If the point (2a,a) lies inside the para...

If the point `(2a,a)` lies inside the parabola `x^(2) -2x - 4y +3 = 0`, then a lies in the interval

A

`[(1)/(2),(3)/(2)]`

B

`((1)/(2),(3)/(2))`

C

`(1,3)`

D

`((-3)/(2),(-1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
The parabola is `(x-1)^(2) =4 (y-(1)/(2))` and origin lies outside the parabolic region, (0,0) makes `x^(2) - 2x - 4y +3` positive.
`:. (2a,a)` should make `x^(2) -2x -4y +3` negative i.e., `4a^(2) - 8a + 3 lt 0`
`rArr (2a-1) (2a-3) lt 0`
Thus, a belongs to the open interval `((1)/(2),(3)/(2))`.
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