Question

(d) Find the radius of curvature at origin of the curve
x - 3x²y + 4xy2 - 4y +6x² - 8xy +9y-6y=0​

Answer 1

$x - 3 {x}^{2} y + 4xy {}^{2} - 4y + 6 {x}^{2} - 8xy + 9y - 6y = 0$

$3xy + 4xy {}^{2} - 10 {x}^{2} y - 8xy + 3 = 0$

$7 {x}^{2} {y}^{3} - 2x + 3 = 0$

$9xy {}^{3} + 3 = 0$

$11x {y}^{3} = 0$

$xy {}^{3} = 0 - 11$

$xy {}^{3} = - 11$