The line `x = at^(2)` meets the ellipse `x^(2)/a^(2) + y^(2)/b^(2) = 1` in the real points iff

Options

A. `|t| lt 2`
B. `|t| le 1`
C. `|t| gt t`
D. none of these

Answer

B

Explanation

Putting `x = at^(2)` in the equation of the ellipse, we get
`(a^(2) t^(4))/(a^(2)) + y^(2)/b^(2) = 1 rArr y^(2) = b^(2) (1 - t^(4)) = b^(2) (1 - t^(2))(1 + t^(2))`
This will gives real values of y if `1 - t^(2) ge 0 rArr |t| le 1`