Conics Hyperbola Question (1 Viewer)

[Vizsla]

Here is the question.

P is a variable point on the standard hyperbola with focus S. PT is tangent at P and ST is perpendicular to PT.

Show that T lies on the circle x^2 + y^2 = a^2.

any help is appreciated

 

[dan964]

I'll give you steps instead...
1. Let P represent (a sec theta, b tan theta)
2. Find dy/dx, and sub P into to find gradient of PT. Find equation of PT
3. Find equation of PS, using S as the point, and -1/m as the gradient, where m is the gradient of PT.
4. Solve equations from (2) and (3) simulateneously to find co-ordinates of T.
5. Eliminate the parameter (theta) by substitution into given result or otherwise.

 

[Vizsla]

I'll give you steps instead...
1. Let P represent (a sec theta, b tan theta)
2. Find dy/dx, and sub P into to find gradient of PT. Find equation of PT
3. Find equation of PS, using S as the point, and -1/m as the gradient, where m is the gradient of PT.
4. Solve equations from (2) and (3) simulateneously to find co-ordinates of T.
5. Eliminate the parameter (theta) by substitution into given result or otherwise.

Did you go to sydney tech?

 

[enigma_1]

Did you go to sydney tech?

Yeah

 

[dan964]

yes I did