Homework SourseThe equation y x2 x y2 12 defines a curve implicitly Find
The equation y x2 + x y2 = 12 defines a curve implicitly. Find the equation of the normal to the curve at the point (1,3).
Implicitly differentiate the equation with respect to x to produce an equation involving x, y and y\'
Equation:
Implicitly differentiate the equation with respect to x to produce an equation involving x, y and y\'
Equation:
Solution
as f(x)g(x) differential = f(x)g\'(x)+g(x)f\'(x)
differenciating we get
2yx+x2y\'+2xyy\'+y2=0
so y\'=-y(2x+y)/(x(x+2y))
