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

x+y-ln(x+y)=2x+5 has a vertical tangent at the point (alpha,beta) then alpha+beta is equal to

If the image of the point ( 1,-2,3) in the plane 2x + 3y -z =7 is the point ( alpha, beta , gamma ), then the value of alpha + beta + gamma is equal to

The graph of 2x=5-3y cuts the x-axis at the point P(alpha,beta) . The value of (2alpha+beta) is :

The graph of 2x = 5-3y cuts the x-axis at the point P( alpha,beta ). The value of (2alpha+beta) is

I If a point (alpha,beta) lies on the circle x^(2)+y^(2)=1 then the locus of the point (3 alpha.+2,beta), is

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 the tangent to the curve y= (x)/(x^(2) - 3), x in r ( xne pm sqrt3) , at a point (alpha, beta ) ne (0, 0) on it is parallel to the line 2x + 6y -11 =0 , then (A) |6alpha + 2beta|=19 (B) |6alpha + 2 beta|=9 (C) |2 alpha + 6 beta |= 19 (D) | 2 alpha + 6 beta| = 11

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 ______