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

@shubhamsrg

dy/dx = -4y/5x

Answer 2

@shubhamsrg

Answer 3

let it cut the axes at (a,0) and (0,b)

then b/a = 4y/5x

Let the ratio be k:1


then
x = a/(k+1)
and
y = bk/(k+1)

=> x/y = a/bk
=> k= ay/bx

we know ay/bx =5/4

hence k = 5/4