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 \( a>b \).
Ellipse Geometry
(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 \(x^2 + y^2 = a^2 \).

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