Mathematics - Application of Derivative Question with Solution | TestHub

Let $P_1=\left(t_1,t_1^3\right),P_2=\left(t_2,t_2^3\right),P_3=\left(t_3,t_3^3\right)\dots \dots$. Solving tangent equation at $P_1$ with the curve again we get $t_2=-2t_1$. Repeating the process we have $t_3=4t_1$, $\begin{array}{rlr}& t_4=-8t_1\cdots \cdots \cdots \cdots \cdots & \therefore \frac{\Delta P_1{P}_2{P}_3}{\Delta P_2{P}_3{P}_4}=\left|\begin{array}{lllcccc}{t}_1& t_1^3& 1t_2& t_2^3& 1t_3& t_3^3& 1\end{array}\right|÷\left|\begin{array}{lllcccc}{t}_2& t_2^3& 1t_3& t_3^3& 1t_4& t_4^3& 1\end{array}\right|=\frac{1}{16}\end{array}$