[" If the tangent to the curve "],[2y^(3)=ax^(2)+x^(3)" at the point "(a,a)" cuts off "],[" intercepts,"alpha" and "beta" on the coordinate "],[" axes such that "alpha^(2)+beta^(2)=61," then "a=]

If the tangent to the curve 2y^(3)=ax^(2)+x^(3) at the point (a,a) cuts off intercept alpha and beta on the co-ordinate axes , (where alpha^(2)+beta^(2)=61 ) then a^(2) equals ______

If the tangent to the curve 2y^(3)=ax^(2)+x^(3) at the point (a,a) cuts off intercept alpha and beta on the co-ordinate axes , (where alpha^(2)+beta^(2)=61 ) then a^(2) equals ______

If the tangent to the curve 2y^(3)=ax^(2)+x^(3) at the point cuts off intercepts alpha and beta on the coordinate axes, where alpha^(2)+beta^(2)=61 then the value of |a| is

If the tangent to the curve 2y^3=ax^2+x^3 at the point (a,a) cuts off Intercepts alpha and beta on the coordinate axes, (where alpha^2+beta^2=61) then the value of a is

If tangent to curve 2y^(3)=ax^(2)+x^(3) at point (a,a) cuts off intercepts alpha,beta on co-ordinate axes,where alpha^(2)+beta^(2)=61, then the value of 'a' is equal to (A) 20 (B) 25 (C) 30 (D)-30

If tangent to curve 2y^3 = ax^2+ x^3 at point (a, a) cuts off intercepts alpha, beta on co-ordinate axes, where alpha^2 + beta^2=61 , then the value of 'a' is equal to (A) 20 (B) 25 (C) 30 (D)-30

Show that the lenght of the portion of the tangent to the curve x^(2/3)+y^(2/3)=a^(2/3) at any point of it, intercept between the coordinate axes is contant.

Find the equation of the tangent to the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) at the point (alpha,beta)

The abscissa of the point on the curve ay^(2)=x^(3) , the normal at which cuts off equal intercepts from the coordinate axes is

The abscissa of the point on the curve ay^(2)=x^(3), the normal at which cuts off equal intercepts from the coordinate axes is