If the tangent drawn to the curve `y=x^(3)+3x^(2)+2x+2" at "(0,2)` also touches the curve `y=kx^(2)` at `(alpha,beta),` then absolute value of `(alpha+(beta)/(k))` equal to

If a tangent is drawn parallel to the line 6x+18y-11=0 to the curve y=(x)/(x^(2)-3) which touches the curve at point (alpha,beta) then

If x+4y=14 is a normal to the curve y^(2)=alpha x^(3)-beta at (2,3), then the value of alpha+beta is 9(b)-5(c)7(d)-7

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 (alpha,beta) is the centre of the circle which touches the curve x^(2)+xy-y^(2)=4 at (2,2) and the line 3x-y+6=0 ,then the value of alpha+beta is equal to

If a tangent drawn at P(alpha, alpha^(3)) to the curve y=x^(3) meets it again at Q(beta, beta^(3)) , then 2beta+alpha is equal to

If the point on the curve y ^(2) = 6x, nearest to the point ( 3, (3)/(2)) is ( alpha, beta) then 2 ( alpha + beta) is equal to _________.

The acute angles between the curves y=2x^(2)-x and y^(2)=x at (0, 0) and (1, 1) are alpha and beta respectively, then

If alpha, beta are the roots of equation 3x^(2)-4x+2=0 , then the value of (alpha)/(beta)+(beta)/(alpha) is