Question

What is Directrix in Conic Section?

Answer 1

Directrix in Conic Section

• The directrix of a conic section is a perpendicular line to the axis which defines a conic section together with the focus.
• The distance of the locus of points from the focus is proportional to its horizontal distance from the directrix and $r$is the proportionality constant.
• $\frac{\mathrm{Distance}\mathrm{from}\mathrm{locus}\mathrm{of}\mathrm{a}\mathrm{point}\mathrm{to}\mathrm{focus}}{\mathrm{Distance}\mathrm{from}\mathrm{locus}\mathrm{of}\mathrm{a}\mathrm{point}\mathrm{to}\mathrm{directrix}}=r$

1. If $r=1,$the conic is a parabola.
2. If $r<1,$the conic is an ellipse.
3. If $r>1,$the conic is a hyperbola.