Practicing Success
The angle between three curves $xy =\sqrt{2}$ and $x^2-y^2=1$ at $(\sqrt{2}, 1)$ is : |
30° 45° 60° 90° |
90° |
The correct answer is Option (4) → 90° $xy =\sqrt{2}$ $x^2-y^2=1$ $P(\sqrt{2}, 1)$ Differentiating both equation wrt x $y+x\frac{dy}{dx}=0$ $\frac{dy}{dx}=-\frac{y}{x}⇒\left.\frac{dy}{dx}\right]_{(\sqrt{2}, 1)}=-\frac{1}{\sqrt{2}}$ $2x-2y\frac{dy}{dx}=0$ $\frac{dy}{dx}=\frac{x}{y}$ $\left.\frac{dy}{dx}\right]_{(\sqrt{2}, 1)}=\sqrt{2}$ so $-\frac{1}{\sqrt{2}}×\sqrt{2}=-1$ so both are inclined at 90° |