1

For a parabola $y^2 = 4ax$ ,we can draw $2$ tangents from any point.If the point is outside of parabola then obviously we can draw $2$ tangents. If the point is on the parabola then the two tangents will coincide and it is easy to draw that picture. I know that if the point is inside the parabola then the tangents are imaginary.

But What does it means that the tangents are imaginary ? And I don't know how it will draw?

JKnecht
  • 6,543
A R
  • 237
  • 2
    Tangents being imaginary is not a literal thing. It just means you're taking the square root of a negative number. It's not possible to draw anything in this case. Think of finding the intersection of a parabola with the $x$-axis. Imaginary solutions means that there is no intersection. If you find the equations of the tangents for an arbitrary point $(a,b)$, you'll find that when $(a,b)$ is inside the parabola you are taking the square root of something which is negative. – Oliver Jones Feb 08 '16 at 02:24
  • @OliverJones: But then what is the logic to say that there are 2 tangents though the point is inside the parabola? – A R Feb 08 '16 at 02:31
  • 1
    It makes no sense to say that there are 2 imaginary tangents. What they really mean is that they got imaginary slopes for the lines. – Oliver Jones Feb 08 '16 at 02:32

0 Answers0