Question

The angle between curves $y^2=4x$ and $x^2+y^2=5$ at (1,2) is

• A. $ta{n}^{-1}\left(3\right)$
• B. $ta{n}^{-1}\left(2\right)$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is A $ta{n}^{-1}\left(3\right)$

For curve $y^2=4x\Rightarrow \frac{dy}{dx}=\frac{4}{2y}$
$\therefore {\left(\frac{dy}{dx}\right)}_{(1,2)}=1$ and for curve $x^2+y^2=5\Rightarrow \frac{dy}{dx}=\frac{-x}{y}$
$\therefore {\left(\frac{dy}{dx}\right)}_{(1,2)}=\frac{-1}{2}$
$\therefore$ Angle between the curves is
$\theta =ta{n}^{-1}\left|\frac{\frac{-1}{2}-1}{1+\left(\frac{-1}{2}\right)}\right|=ta{n}^{-1}\left(3\right)$