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**1. The problem statement, all variables and given/known data**

Prove that the straight line x cos @ + y sin @ = p is a tangent to the ellipse x

^{2}/a

^{2}+ y

^{2}/b

^{2}if a

^{2}cos

^{2}@ + b

^{2}sin

^{2}@ =p

^{2}.

u and v are the perpendicular distances of a tangent from the two points M(0,ae) and N(0,-ae) respectively. Prove that u

^{2}+ v

^{2 }is a constant.

**2. The attempt at a solution**

So far I have: xx

_{1}/a

^{2}+yy

_{1}/b

^{2}-1 = x cos@ + y sin@ - p

I don't know where to go from here and I know in the second part I have to use the perpendicular distance formula but I'm not sure what to sub in and why.

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