本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
Consider the curves )v3bfd.oe2xe 9lcmy23 h xsl* x98z6h ygf(ug pb x*3h$C_{1}$ and $C_{2}$ defined as follows
$\begin{array}{l}
C_{1}: \quad 3 y^{2}+2 x^{2}=5, y>0 \\
C_{2}: \quad y^{2}-5 x^{3}=0, y>0
\end{array}$
1. Using implicit differentiation, or otherwise, find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ for each curve in terms of x and y .
Let $\mathrm{P}(a, b)$ be the unique point where the curves $C_{1}$ and $C_{2}$ intersect.
2. Show that the tangent to $C_{1}$ at P is perpendicular to the tangent to $C_{2}$ at P .
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