Hard conics Question (1 Viewer)

[Praer]

Equation of Hyperbola : x²/a² -y²/b² = 1
Normal: (yy₁)/a²- xx₁/b² = 1

The normal at P(x₁,y₁) meets the x-axis at G, and N is the foot of the perpendicular from P to the x-axis. Show that NG:ON = b²:a², where O is the origin.

Need some help -.-

 

[Nws m8]

It's not a hard question, it's a typical HSC question,

Find the coordinates of G and N, find the distance NG and ON .... And divde NG by ON

And the is an easy way to find NG and ON, rather than using the distance formula, I'm sure you know that

 

[Praer]

The co-ordinates are x= -a^2/x1 for G and x = x1 for N
And in ratio i get (-a^2 - x1^2 = x1^2)
how am i suppose to make this equation into a^2 = b^2 ...

It's not a hard question, it's a typical HSC question,

Find the coordinates of G and N, find the distance NG and ON .... And divde NG by ON

And the is an easy way to find NG and ON, rather than using the distance formula, I'm sure you know that

 

[Nws m8]

Equation of Hyperbola : x²/a² -y²/b² = 1
Normal: (yy₁)/a²- xx₁/b² = 1

The normal at P(x₁,y₁) meets the x-axis at G, and N is the foot of the perpendicular from P to the x-axis. Show that NG:ON = b²:a², where O is the origin.



Need some help -.-

Your "equation of normal" is the equation of tangent
The question is wrong

 

[Praer]

Your "equation of normal" is the equation of tangent
The question is wrong

God DAMNIT! THIS QUESTION TOOK ME 2 HOURS SO FAR -.-"
Ugh... So frustrated!
tnx btw

 

[Nws m8]

God DAMNIT! THIS QUESTION TOOK ME 2 HOURS SO FAR -.-"
Ugh... So frustrated!
tnx btw

Lol did you get the right answer ?

 

[Praer]

Lol did you get the right answer ?

Yep, just finished it. Tnx

 

[Nws m8]

Yep, just finished it. Tnx

No worries