Question

The angle of intersection of the curves $xy=a^2$ and $x^2-y^2=2a^2$ is

• A. $0^o$
• B. ${45}^o$
• C. ${90}^o$
• D. ${30}^o$

Answer 1

The correct option is C ${90}^o$

$xy=a^2$ ..........$\left(1\right)$

$x^2-y^2=2a^2$ .........$\left(2\right)$

Let (h, k) be the point of intersection of the two curves.

Differentiating eq $\left(1\right)$, we get

$x{y}^{\prime }+y=0$

$\Rightarrow y^{\prime }=-\left(y/x\right)=-\left(k/h\right)=m_1$ at $(h,k)$

Differentiating eq $\left(2\right)$, we get

$2x-2y{y}^{\prime }=0$

$\Rightarrow y^{\prime }=\left(x/y\right)=\left(h/k\right)=m_2$ at $(h,k)$

Slopes at (h, k) for both the curves

$m_1\times m_2=-1$

Hence, intersection angle of curves is ${90}^o$.