Hello.

Could someone please explain to me how to do the parts regarding the angle x??? (I've already sketched the ellipse, hyperbola + common auxillary circles.)

Sketch the ellipse $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2}=1$, the hyperbola $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2}=1$and their common auxillary circles $\displaystyle x^2 + y^2 = a^2$ and $\displaystyle x^2 + y^2 = b^2$ on the same diagram, showing the angle x and the related points P(acosx, bsinx) - a point in the 1st quadrant on the ellipse - and Q (asecx, btanx) - a point on the hyperbola. Show clearly how the positions of P and Q are determined by the value of x where 0<x<90 degrees.