Standard +0.3 This is a straightforward implicit differentiation question requiring students to differentiate implicitly, substitute a point to find the gradient, then find the normal equation. While it involves multiple steps, each is routine for C4 level with no conceptual challenges beyond standard technique application.
3. A curve has the equation
$$3 x ^ { 2 } + x y - 2 y ^ { 2 } + 25 = 0$$
Find an equation for the normal to the curve at the point with coordinates \(( 1,4 )\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
3. A curve has the equation
$$3 x ^ { 2 } + x y - 2 y ^ { 2 } + 25 = 0$$
Find an equation for the normal to the curve at the point with coordinates $( 1,4 )$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.\\
\hfill \mbox{\textit{OCR C4 Q3 [7]}}