The points on the curve 4x2 +9y2 = ...
Question
Fullscreen

The points on the curve 4x2 +9y2 = 1, at which the tangents are parallel to the line 8x = 9y are

JEE/Engineering Exams
Maths
Solution
99
Rating
4.0 (1 ratings)
Fullscreen
( 4 x^{2}+9 y^{2}=1 ) Differentiating both sides. [ begin{array}{l} 8 x+18 y frac{d y}{d x}=0 frac{d y}{d x}=frac{-8 x}{18 y}=frac{-4 x}{9 y} end{array} ] ( therefore ) slope of tangent at point ( (x, y), m_{T}=left[frac{d y}{d x}right] ) [ =-frac{4 x}{9 y} ] given line ( : 8 x=9 y ) [ begin{aligned} therefore quad 8 &=9 frac{d y}{d x} frac{d y}{d x} &=frac{8}{9} end{aligned} ] ( Rightarrow quad m_{T}=frac{8}{9} ) ( r: ) line & tangew [ begin{array}{l} frac{8}{80,}=-frac{4 x}{9 y} Rightarrow 4 x=-8 y x=-2 y end{array} ] since this point lies on ginen curare ( 4(-2 y)^{2}+9 y^{2}=1 Rightarrow y=pm frac{1}{5} ln x=pm frac{2}{5} )
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free