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Show that the line xcosalpha+y sinalpha+...

Show that the line `xcosalpha+y sinalpha+p` touches the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` if `a^(2)cos^(2)alpha=b^(2)sin^(2)alpha=p^(2)` and the point of contact is `(a^(2)cosalpha/p),(b^(2)sinalpha/p)`.

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