Conics help please (1 Viewer)

Aysce · Mar 15, 2012

Screen shot 2012-03-15 at 10.36.21 PM.png

I just need help with iii or just a hint will do. Thanks to all who help.

P.S: Can someone tell me how to insert pictures without attachments, I've been searching for ages on how to but couldn't find out.

IamBread · Mar 15, 2012

Drongoski · Mar 15, 2012

Aysce said:
View attachment 24598

I just need help with iii or just a hint will do. Thanks to all who help.

P.S: Can someone tell me how to insert pictures without attachments, I've been searching for ages on how to but couldn't find out.

It is easier and smarter to show that the co-ords of T satisfy the eqns of tangents at P and at Q. Usually much harder to do it by finding the co-ords of point of intersection of the two tangents(by solving for simultaneous eqns).

For example, for tangent at P:

$LHS = x + t_1 ^2y = \frac {2ct_1 t_2}{t_1 + t_2} + t_1 ^2 (\frac {2c}{t_1 + t_2}) = \frac {2ct_1 (t_1 + t_2)}{t_1 + t_2} = 2ct_1 = RHS$

IamBread · Mar 15, 2012

Drongoski said:
It is easier and smarter to show that the co-ords of T satisfy the eqns of tangents at P and at Q. Usually much harder to do it by finding the co-ords of point of intersection of the two tangents. e.g. for tangent at P:

$LHS = x + t_1 ^2y = \frac {2ct_1 t_2}{t_1 + t_2} + t_1 ^2 (\frac {2c}{t_1 + t_2}) = \frac {2ct_1 (t_1 + t_2)}{t_1 + t_2} = 2ct_1 = RHS$

Yeah that is a better way.

Aysce · Mar 15, 2012

Wow? Tried for Point of intersection but failed miserably

Thanks Drongo!

Drongoski · Mar 16, 2012

Aysce said:
Wow? Tried for Point of intersection but failed miserably Thanks Drongo!

For this particular question, finding point of intersection is not that much harder though.

$x + t_1 ^2y = 2ct_1$

$x + t_2 ^2 y = 2ct_2$

$\therefore 2ct_1 - t_1^2 y = 2ct_2 - t_2^2y \implies (t_1 ^2 - t_2^2)y = 2c(t_1 - t_2)$

$\implies y = \frac {2c(t_1 - t_2)}{t_1 ^2 - t_2 ^2} = \frac {2c}{t_1 + t_2}$

$\therefore x = 2ct_1 - t_1 ^2 y = 2ct_1 - t_1 ^2 (\frac {2c}{t_1+t_2}) = \frac {2ct_1t_2}{t_1+t_2}$

Aysce · Mar 16, 2012

Conics help please (1 Viewer)

Aysce

Well-Known Member

IamBread

Member

Drongoski

Well-Known Member

IamBread

Member

Aysce

Well-Known Member

Drongoski

Well-Known Member

Aysce

Well-Known Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)