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\includegraphics[max width=\textwidth, alt={}, center]{df94bc38-5187-4349-9005-f9b72691c70d-4_519_770_251_242}
A student wishes to model the saddle of a horse. They use a surface described by a function of the form \(\mathrm { z } = \mathrm { f } ( \mathrm { x } , \mathrm { y } )\) with a saddle point at the origin \(O\). The z -axis is vertically upwards. The \(x\) - and \(y\)-axes lie in a horizontal plane, with the \(x\)-axis across the horse and the \(y\)-axis along the length of the horse (see diagram).
The arc \(A O B\) is part of a parabola which lies in the \(y z\)-plane. The arc \(C O D\) is part of a parabola which lies in the \(x z\)-plane. The saddle is symmetric in both the \(x z\)-plane and \(y z\)-plane.
The length of the saddle, the distance \(A B\), is to be 0.6 m with both \(A\) and \(B\) at a height of 0.27 m above \(O\). The width of the saddle, the distance \(C D\), is to be 0.5 m with both \(C\) and \(D\) at a depth of 0.4 m below \(O\).
- On separate diagrams, sketch the sections \(x = 0\) and \(y = 0\).
[0pt] - Determine a function f that describes the saddle. [You do not need to state the domain of function f .]
\section*{END OF QUESTION PAPER}
\section*{OCR
Oxford Cambridge and RSA}