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 (alpha,alpha) is a point on the circle whose centre is on the x -axis and which touches the line x+y=0 at (2,-2), then the greatest value of 'alpha' is

If the point (2 , alpha , beta) lies on the plane which passes through the points (3,4,2) and (7,0,6) and is perpendicular to the plane 2x-5y=15, then 2 alpha - 3 beta is equal to:

Let the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2) lie in the plane x+3y-alpha z+ beta=0 then the value of alpha+beta=

" The point on the curve "xy^(2)=1" ,which is nearest to the origin is "(alpha,beta)" then the value of "| alpha beta|" equals "

The centre of the circle (x-a)^(2)+(y-3)^(2)=9 lies on the straight line x=y and the circle touches the circle x^(2)+y^(2)=1 externally.What are the values of alpha,beta?

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 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

Consider a circle (x-alpha)^(2)+(y-beta)^(2)=50 ,where alpha,beta>0 .If the circle touches the line y+x=0 at the point "P" ,whose distance from the origin is 4sqrt(2) ,then (alpha+beta)^(2) 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 _________.

If alpha and beta are the roots of x^(2)-2x+4=0 then the value of alpha^(6)+beta^(6) is