Conics question help (1 Viewer)

[s8891]

1. S is a focus of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = . The tangent at (a,0) meets an asymptote at the point T. Show that OT=OS

2. Show that the chord of tangent of the tangent from a point on a directrix of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 is a focal chord through the corresponding focus.

3. Show that the tangents at the end points of a focal chord of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 meet the corresponding directrix.

I always get spooked by questions which ask to show something


thanks

 

[Carrotsticks]

I'll get you started for the mean time and if I have time, I'll do a set of solutions for you tomorrow.

1. OS is obviously length 'a'. Find the equation of the tangent and solve simultaneously with the equation of the asymptote it intersects (this is point T). Use distance formula (or Pythagoras' Theorem, same thing) to find the distance OT and show that it's 'a'.

2. Find the equation of this chord and sub in (a,0) and show that the point satisfies the equation (ie: the chord passes through it).

3. Find the point of intersection of the tangents and show that the x coordinate is the same thing as the x coordinates of the directrix (hence it meets on the directrix. Y value doesn't matter).

Good luck =)

 

[s8891]

thanks starting tips
should be able to do it now