The tangent of the angle between the curves xy=1 and x^2+8y=0, is

Question

Accepted Answer

Correct answer: C. (c) We have xy=1 and x^2+8y=0 Slope of the curve xy=1 x dy dx+y=0 ⇒m_1= dy dx= -yx………(i) Slope of the curve 2x+ 8 dy dx=0 m_2= dy dx= -2x8= -x4……….(ii) ⇒x^2+ 8x=0 ⇒x^3+8=0 ⇒ (x^3 )+ (2 )^3=0 (x+2 )(x^2+4+2x)=0x+2=0 ⇒x=-2 From curve xy=1 ⇒y= -12 (x ,y ) (-2 , -12)m_1= - ( -12 ) (-2 )= -14m_2= 24= 12 tan ⁡ = ( 12+ 141- 18 )= 67

$The tangent of the angle between the curves xy = 1 and x^{2} + 8 y = 0, is$

Solution

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