Review question

# Where does this chord of an ellipse cut the $x$-axis? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6843

## Question

Prove that the equation of the chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ joining the points $(a\cos\alpha,b\sin\alpha)$ and $(a\cos\beta,b\sin\beta)$ is $\frac{x}{a}\cos\left(\frac{\alpha+\beta}{2}\right)+\frac{y}{b}\sin\left(\frac{\alpha+\beta}{2}\right)= \cos\left(\frac{\alpha-\beta}{2}\right).$

Through a point $P$ on the major axis of an ellipse a chord $HK$ is drawn. Prove that the tangents at $H$ and $K$ meet the line through $P$ at right angles to the major axis at points equidistant from $P$.