If 2x + 3y + 12 = 0 and x - y + 4 = 0 are conjugate with respect to the parabola y = 8x, then is equal to
2
- 2
3
- 3
For an ellipse with eccentricity the centre is at the origin. If one directrix is x = 4, then the equation of the ellipse is
If : RC is defined by f(x) =eix for x ∈ R, then f is (whereC denotes the set of all complex numbers)
one-one
onto
one-one and onto
neither one-one nor onto
D.
neither one-one nor onto
Given that, f(x) = e2ix and f: RC.
Function f(x) is not one-one, because after some values of x (ie, π) it will give the same values.
Also, f(x) is not onto, because it has minimum and maxinmm values - 1 - i and 1 + i respectively.
Hence, option (d) is correct.