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

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

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

If alpha and beta are the roots of x^(2)-ax+b^(2)=0 , then alpha^(2) +beta^(2) is equal to_______

If alpha and beta are the roots of x ^(2) - ax + b ^(2) = 0, then alpha ^(2) + beta ^(2) is equal to