# Ellipse Geometry

Ellipse Geometry is used for proving ellipse questions relating to geometry such as similar triangles and circle geometry.

### Worked Examples of Ellipse Geometry

The diagram shows the ellipse $$\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$, where $$a>b$$.

(a)    Prove that $$SQ = RQ$$.

(b)    Show $$S’R = 2a$$.

(c)    Prove $$\triangle OSQ$$ and $$\triangle S’SR$$ are similar.

(d)    Prove $$Q$$ lies on the circle $$x^2 + y^2 = a^2$$.