From a point `(sintheta,costheta)`, if three normals can be drawn to the parabola `y^(2)=4ax` then the value of a is

Question

From a point `(sintheta,costheta)`, if three normals can be drawn to the parabola `y^(2)=4ax` then the value of a is

From a point `(sintheta,costheta)`, if three normals can be drawn to the parabola `y^(2)=4ax` then the value of a is
A. (1/2,1)
B. [-1/2,0)
C. [1/2,1]
D. `(-1/2,0cup(0,12))`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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))`

5 views Answered 2023-02-05 15:29