Question

The angle between the tangents to the curves $y=x^2$ and $x=y^2$ at $(1,1)$ is

• A. ${\cos }^{-1}\frac{4}{5}$
• B. ${\sin }^{-1}\frac{3}{5}$
• C. ${\tan }^{-1}\frac{3}{4}$
• D. ${\tan }^{-1}\frac{1}{3}$

Answer 1

Answer: (A), (B), (C)

${\sin }^{-1}\frac{3}{5}$
${\cos }^{-1}\frac{4}{5}$
${\tan }^{-1}\frac{3}{4}$

Slope of tangent to curve $y=x^2$ at $(1,1)$ is $m_1=2$

Slope of tangent to curve $x=y^2$ at $(1,1)$ is $m_2=\frac{1}{2}$

Angle between tangent to the curves is

$tan\theta =\frac{3}{4}$

or $\theta =ta{n}^{-1}\frac{3}{4}$

or $\theta ={\sin }^{-1}\frac{3}{5}$

$\theta ={\cos }^{-1}\frac{4}{5}$