Find the slope of the curve x2 xy y2 7 at 12SolutionThe s

Find the slope of the curve x^2 + xy + y^2 = 7 at (1,2)

The slope of the curve ,x^2+xy+y^2 = 7 at (1,2) is got by diffrentiating both sides of the equation and evaluating dy/dx or y\' at (1,2).

x^2+xy+y^2 = 7

(x^2+xy+y^2)\' = (7)\'

2x+y+y\' +2y*y\' = 0

y\'(1+2y) = -(2x+y)

y\' = -(2x+y)/(1+2y)at(1,2) = -(2*1+2)/(1+2*2)

y\' = -4/5

Slope = y\' = -4/5 at (1,2).