The question is
![](https://latex.codecogs.com/png.latex?\bg_white $P%20$%28a%20cos%5Ctheta,%20bsin%5Ctheta%29$%20and%20Q%20$[a%20cos%20%28%5Ctheta+%20%5Cpi%29,%20bsin%20%28%5Ctheta+%5Cpi%29]$%20lies%20on%20the%20ellipse%20$%20%5Cfrac%7Bx%5E2%7D%7Ba%5E2%7D+%5Cfrac%7By%5E2%7D%20%7Bb%5E2%7D=1%20$%20Show%20that%20PQ%20passes%20through%20%280,0%29$)
Letting (θ+ pi) = ɸ
I found the gradient of the chord, then the equation of it, cleaned it up but ended up getting
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7Bx%7D%7Ba%7Dcos%28%5Cfrac%7B%5Ctheta+%20%5Cphi%20%7D%7B2%7D%29-%20%5Cfrac%7By%7D%7Bb%7Dsin%28%5Cfrac%7B%5Ctheta+%20%5Cphi%20%7D%7B2%7D%29=%20cos%5Ctheta%20%5Cfrac%7B%5Ctheta%20+%20%5Cphi%7D%20%7B2%7D-sin%20%5Ctheta%20%5Cfrac%7B%5Ctheta%20+%20%5Cphi%7D%20%7B2%7D)
giving
![](https://latex.codecogs.com/png.latex?\bg_white %5Cfrac%7Bx%7D%7Ba%7Dcos%28%5Cfrac%7B%5Ctheta+%20%5Cphi%20%7D%7B2%7D%29-%20%5Cfrac%7By%7D%7Bb%7Dsin%28%5Cfrac%7B%5Ctheta+%20%5Cphi%20%7D%7B2%7D%29=%20cos%28%5Ctheta%20+%20%5Cfrac%7B%5Cphi+%5Ctheta%7D%7B2%7D%29)
but as ɸ = (θ+ pi)
the RHS is then
whereas i think it should be ![](https://latex.codecogs.com/png.latex?\bg_white cos%20%5Cfrac%7B%5Cpi%7D%20%7B2%7D)
I don't know what i did wrong or what i'm meant to do next
Edit : This 4U Cambridge 3.2 Q3 btw
Letting (θ+ pi) = ɸ
I found the gradient of the chord, then the equation of it, cleaned it up but ended up getting
giving
but as ɸ = (θ+ pi)
the RHS is then
I don't know what i did wrong or what i'm meant to do next
Edit : This 4U Cambridge 3.2 Q3 btw
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