# Thread: Help with Conics & Parametrics

1. ## Help with Conics & Parametrics

Whats the difference?
latex.png FullSizeRender (1).jpg

2. ## Re: HSC 2017 MX2 Marathon

Originally Posted by Commando007
Whats the difference?
latex.png FullSizeRender (1).jpg
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

3. ## Re: HSC 2017 MX2 Marathon

How do we get this equation
File_000 (1).jpeg

4. ## Re: HSC 2017 MX2 Marathon

Originally Posted by Commando007
How do we get this equation
File_000 (1).jpeg
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.

5. ## Re: HSC 2017 MX2 Marathon

Originally Posted by Rathin
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?

6. ## Re: HSC 2017 MX2 Marathon

Originally Posted by Rathin
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)

7. ## Re: HSC 2017 MX2 Marathon

Originally Posted by tsoliman1
Couldn't the first one also be the equation of the tangent to an ellipse given point that lies on it (x0,y0)
yes

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