# Thread: Sketching Ellipses + Hyperbolas

1. ## Sketching Ellipses + Hyperbolas

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.

2. It's not at all clear what you are asking. You appear to be using "x" with two different meanings.

3. Oops. So sorry!

Sketch the ellipse , the hyperbola and their common auxillary circles and on the same diagram, showing the angle $\displaystyle \theta$and the related points P(acos$\displaystyle \theta$, bsin$\displaystyle \theta$) - a point in the 1st quadrant on the ellipse - and Q (asec$\displaystyle \theta$, btan$\displaystyle \theta$) - a point on the hyperbola. Show clearly how the positions of P and Q are determined by the value of $\displaystyle \theta$ where 0<$\displaystyle \theta$<90 degrees.

4. Hmmm so I've found how to situate the point P on the diagram but im still stuck with Q. Any help please?