Help with Conics & Parametrics (1 Viewer)

[Commando007]

Whats the difference?

 

[Green Yoda]

Re: HSC 2017 MX2 Marathon

Whats the difference?
View attachment 33818 View attachment 33819

The first one is the equation of chord of contact to an ellipse from a point T(x0,y0).
The second one is an equation of the chord from points P(acosθ,bsinθ) and Q(acosφ,bsinφ) in an ellipse

 

[Commando007]

Re: HSC 2017 MX2 Marathon

How do we get this equation

 

[seanieg89]

Re: HSC 2017 MX2 Marathon

How do we get this equation
View attachment 33822

It's most instructive for you to prove these yourself so I will just provide some hints.

Consider the forms of sin(X+Y), sin(X-Y), cos(X+Y), cos(X-Y) upon expansion. Is it possible to combine these to obtain products of the form sin(X)cos(Y), sin(X)sin(Y), cos(X)cos(Y) ?

Now choose X and Y appropriately to put these equations in a "sums to products" form.

 

[Commando007]

Re: HSC 2017 MX2 Marathon

The first one is the equation of chord of contact to an ellipse from a point T(x0,y0).
The second one is an equation of the chord from points P(acosθ,bsinθ) and Q(acosφ,bsinφ) in an ellipse

What is the equation of PQ?
the first image or the second one?

 

[tsoliman1]

Re: HSC 2017 MX2 Marathon

The first one is the equation of chord of contact to an ellipse from a point T(x0,y0).
The second one is an equation of the chord from points P(acosθ,bsinθ) and Q(acosφ,bsinφ) in an ellipse

Couldn't the first one also be the equation of the tangent to an ellipse given point that lies on it (x0,y0)

 

[dan964]

Re: HSC 2017 MX2 Marathon

Couldn't the first one also be the equation of the tangent to an ellipse given point that lies on it (x0,y0)

yes