Question

lf $\alpha$ is the angle between the curves $y^2=2x$ and $x^2+y^2=8$, then $\tan \alpha$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

$y^2=2x$,
$x^2+y^2=8$
$x^2+2x-8=0$
$x=2,x=-4$
$y{=}_{-}^{+}2$
$2y{y}^{\prime }=2$
$y^{\prime }=\frac{1}{y}$
$y^{\prime }=\frac{1}{2}=m_1$
$y^{\prime }=-\frac{x}{y}$
$y^{\prime }=-1=m_2$
$tan\theta =\frac{m_2-m_1}{1+m_1{m}_2}$
$tan\theta =\frac{1+\frac{1}{2}}{1-\frac{1}{2}}$
$tan\theta =3$
$tan\alpha =3$