The point of intersection of the pair of lines `x^(2)+xy+2y^(2)-3x+2y+4=0` is `(alpha,beta)`then `2 alpha+beta=`

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 two lines 2x^(2)-3xy+y^(2)=0 makes anlges alpha and beta with X-axis then : csc^(2) alpha+csc^(2)beta=

Consider the equation of a pair of straight lines as x^2-3xy+lambday^2+3x=5y+2=0 The point of intersection of line is (alpha, beta) , then the value of alpha^2+beta^2 is

If the point (3, 4) lies on the locus of the point of intersection of the lines x cos alpha + y sin alpha =a and x sin alpha - y cos alpha =b ( alpha is a variable), the point (a, b) lies on the line 3x-4y=0 then (a^(2)-b^(2))/2 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

At the point of intersection of the curves y^2=4ax" and "xy=c^2 , the tangents to the two curves make angles alpha" and "beta respectively with x-axis. Then tan alpha cot beta=

For real numbers alpha and beta ne 0 , if the point of intersection of the straight lines ( x - alpha)/( 1) = ( y - 1)/( 2) = ( z -1)/( 3) and ( x - 4) / ( beta) = ( y - 6)/( 3) = ( z - 7)/(3) , lies on the plane x + 2y - z = 8 then alpha - beta is equal to

If x^(2)+4y^(2)=4 and range of f(x,y)=x^(2)+y^(2)-xy is [alpha,beta] .Find the product (alpha beta)

If x^(2)-2cos alpha x+1=0 and y^(2)-2cos alpha y+1=0 then 2cos(alpha+beta)=