The path of a light ray reflected off a curved mirror is modeled by the equation

5\sec^2 2y, \quad x > 5, \quad 0 < y < \frac{\pi}{4}

Find $dxdy\displaystyle \frac{\text{d}x}{\text{d}y}$ in terms of $y$ .

Hence show that

\frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-5}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

Find the equation of the normal to the path at the point where $y=π12\displaystyle y = \frac{\pi}{12}$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are exact constants.

The path of a light ray reflected off a curved mirror is modeled by the equation

5\sec^2 2y, \quad x > 5, \quad 0 < y < \frac{\pi}{4}

Find $dxdy\displaystyle \frac{\text{d}x}{\text{d}y}$ in terms of $y$ .

Hence show that

\frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-5}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

Find the equation of the normal to the path at the point where $y=π12\displaystyle y = \frac{\pi}{12}$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are exact constants.

Differentiation

Question 503

Markscheme

Differentiation

Question 503

Markscheme

Differentiation

Question 503

Differentiation Questions

Differentiation

Question 503

Differentiation Questions