The tangent at any point on the curve `x = at^3. y = at^4` divides the abscissa of the point of contact in the ratio m:n, then `|n + m|` is equal to (m and n are co-prime)

Options

A. `1//4`
B. `3//4`
C. `3//2`
D. `2//5`

Answer

B

Explanation

`(dy)/(dx)=(4t)/(3)`
Tangent is `y-at^(4)=(4t)/(3)(x-at^(3))`
x-intercept`=(at^(3))/(4)`
y-intercept `=(at^(4))/(3)`
the point of intersection of tangent with the axes are `((at^(3))/(4),0) and (0,-(at^(4))/(3))`
`therefore" "(m)/(n)=-(3)/(4)`