Question

The tangent at a point P on the curve x^4 y^5 = a^9 meet the x and y axes in A and B respectively Then AP:PB=?

Answer 1

x^4 y^4 =a^9
d(x^4 y^4)/dx =d(a^9)/dx
d(x^4)/dx *y^4 + x^4 d(y^4)/dx =0
4x^3y^4 +x^4 4y^3 dy/dx=0
dy/dx =-4x^3y^4/(4x^4y^3)
dy/dx =-y/x

Answer 2

Oh...No......There is a mistake in the question Sorry

Answer 3

It is x^4 y^5 = a^9

Answer 4

dy/dx = -4y/5x

Answer 5

x^4 y^5 =a^9
d(x^4 y^5)/dx =d(a^9)/dx
d(x^4)/dx *y^5 + x^4 d(y^5)/dx =0
4x^3y^5+x^4 5y^4 dy/dx=0
dy/dx =-4x^3y^5/(5x^4y^4)
dy/dx =-4y/5x

Answer 6

Now, coordinate of P is