Conics pronlem (1 Viewer)

[vds700]

The equarions of 2 ellipses are:
1)x^2/9 + y^2/4 = 1
2)x^2/15 + y^2/10 = 1

A tangent to ellipse 1 meets ellipse 2 at the points P and Q. Show that the tangents at P and Q to ellipse 2 are perpendicular.

I let the point on the ellipse 1 be (a, b) so that the equation of the tangent through P and Q is

ax/9 + by/4 = 1

I then tried to solve this equation simultaneously with the equation of ellipse 2 but it didn't really work

 

[undalay]

hint:
for the tangent on the smaller circle.
You need to use the general tangent formula.
y=mx+-root(a^2m^2+b^2)

 

[vds700]

wtf? That formula is not in the Fitzpatric k book. I am finding Fitzpatrick is quite hard to worl from. Is Cambridge, Teery Lee, Patel or any others better for Conics than Fitzpatrick?

 

[namburger]

wtf? That formula is not in the Fitzpatric k book. I am finding Fitzpatrick is quite hard to worl from. Is Cambridge, Teery Lee, Patel or any others better for Conics than Fitzpatrick?

let the tangent be y = mx + c
sub it into x^2/a^2 + y^2/b^2 = 1

for there to be tangent, delta = 0
so you find delta and you will find an expression for c
Sub c back into y = mx + c and it will be y=mx+-root(a^2m^2+b^2)
So all tangents to the ellipse will satisfy that equation

 

[vds700]

Thanks man.

How come they don't give you this formula in the book? I checked Cambridge and its not there either

 

[jkwii]

thes kind of Qs are not actually part of the hsc syllabus - its like asking what is the locus of point A if the tangents at P and Q subtend a right angle at A?

if u look at patel there is a whole exercise on these non-syllabus Qs which are very good.. but wont be asked in the hsc