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  • Explain Solution R.D.Sharma Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Questions Question 14 maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Questions Question 14 maths Textbook Solution.

Answers (1)

Answer:

            \left ( c \right )90^{o}

Hint:

          Use differentiation

Given:

            xy=a^{2} Andx^{2}-y^{2}=2a^{2}

Solution:

\begin{aligned} &x y=a^{2} \text { And } x^{2}-y^{2}=2 a^{2} \\ &x \frac{d y}{d x}+y=0 \text { And } 2 x-2 y \frac{d y}{d x}=0 \\ &\frac{d y}{d x}=-\frac{y}{x} \text { And } \frac{d y}{d x}=\frac{x}{y} \end{aligned}

\begin{aligned} &\left(\frac{d y}{d x}\right)_{1}=-\frac{y}{x} \text { And }\left(\frac{d y}{d x}\right)_{2}=\frac{x}{y} \\ &\left(\frac{d y}{d x}\right)_{1} \times\left(\frac{d y}{d x}\right)_{2}=-\frac{y}{x} \times \frac{x}{y}=-1 \end{aligned}

Hence the intersection angle =\frac{\pi }{2}

                

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