Conics - Hyperbola (1 Viewer)

[Lukybear]

When considering hyperbola via parametrics, how come the angle (a) for the RHB is limited to pi/2 - -pi/2 whilst on the LHB, (a) is limited to -pi/2 - -pi and pi-2 - pi

 

[gurmies]

Looks like it has something to do with polar coordinates.

 

[Lukybear]

Using focus - directrix definition, show that PS/PS* = TS/TS*

where S, S* are foci, and T is tangent at P intersecting x-axis

 

[imnotwallace]

I've seen that question in an Ext 2 past paper.

What you do is, in general terms, you find a numerical expression for TS/TS*
T is found earlier in the question, as well as the foci and directrices.
That should be, TS/TS* = - (9/Xo - 4) / (4 + 9/Xo) or something similar...
Now using the definition PS/PS* = PM/PM*, we find the expression for PM/PM* and essentially prove PM/PM* = TS/TS*.
Hence, PS/PS* = TS/TS*