Conics Question (1 Viewer)

[bumpkin]

Find the equation of the tangent at P(a,b) on H: x^2/3 - y^2/2 =1

i) if h,k are the intercepts made by this tangent on the coordinates axes, show that 3/h^2 - 3/k^2 =1

ii) If the lenth of the perpendicular from the origin O to this tangent is p and OP = r
show that 1/p^2 = (r^2 - 1)/6


I CANT DO IT!

 

[Rorix]

you cant do the whole thing?

 

[bumpkin]

well - i cant get the first part out.

 

[ngai]

i) if h,k are the intercepts made by this tangent on the coordinates axes, show that 3/h^2 - 3/k^2 =1

should be 3/h^2 - 2/k^2 =1

 

[bumpkin]

it should!

How did you get it out?

 

[bumpkin]

dudes! please help i cant do this question!

lol


please please please

 

[Bob.J]

Find the equation of the tangent at P(a,b) on H: x^2/3 - y^2/2 =1

i) if h,k are the intercepts made by this tangent on the coordinates axes, show that 3/h^2 - 3/k^2 =1

ii) If the lenth of the perpendicular from the origin O to this tangent is p and OP = r
show that 1/p^2 = (r^2 - 1)/6


I CANT DO IT!

Well i havent done conics for 2 years (since 2002) but lets see
using the equation of a tangent
x.x1/a^2 + y.y1/b^2=1

so at a,b we get the eqn of the tangent to be

ax/3 - by/2 =1

at x-axis we have y=0
so x=3/a but at the x axis it was said that the coords are h,k so you make x=h
this gives us h=3/a
so a=3/h sub that back into the original eqn of the ellipse x^2/3 - y^2/2
and doing the same thing we get y=k=-2/b

so we sub that into x^2/3 - y^2/2 as well
we get the following:

(9/h^2)/3 - (4/k^2)/2 = 1

this gives us the desired eqn of 3/h^2 - 2/k^2=1

and yeah thats that