Question

The angle between the curves $x^2+y^2=25$ and $x^2+y^2-2x+3y-43=0$ at $(-3,4)$ is

• A. ${\tan }^{-1}\left(1\right)$
• B. ${\tan }^{-1}\left(\frac{1}{68}\right)$
• C. $\frac{\pi }{2}$
• D. ${\tan }^{-1}\left(\frac{3}{4}\right)$

Answer 1

Answer: (B)

${\tan }^{-1}\left(\frac{1}{68}\right)$

slope of first curve at $(-3,4)$

$m_1=dy/dx=\frac{-x}{y}=\frac{3}{4}$

slope of second curve at $(-3,4)$

$m_2=\frac{-2x+2}{2y+3}=\frac{8}{11}$

angle between them $=ta{n}^{-1}\frac{m_1-m_2}{1+m_1+m_2}$

$=ta{n}^{-1}\frac{1/44}{17/11}=ta{n}^{-1}\frac{1}{68}$