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 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 tangentat P of the curve y^2 = x^3 intersect the curve again at Q and the straigta line OP, OQ have inclinations alpha and beta where O is origin, then tanalpha/tan beta has the value equals to

The curve x+y-log_(e)(x+y)=2x+5 has a vertical tangent at the point (alpha, beta). then alpha+beta is equal to

If 0

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 the length of the tangent drawn from (alpha,beta) to the circle x^(2)+y^(2)=6 be twice the length of the tangent from the same point to the circle x^(2)+y^(2)+3x+3y=0, then prove that alpha^(2)+beta^(2)+4 alpha+4 beta+2=0

If alpha1=beta but alpha^(2)=2 alpha-3;beta^(2)=2 beta-3 then the equation whose roots are (alpha)/(beta) and (beta)/(alpha) is

If alpha!=beta and alpha^(2)=5 alpha-3 and beta^(2)=5 beta-3. find the equation whose roots are alpha/ beta and beta/ alpha .