If `S_(1)=alpha^(2)+beta^(2)-a^(2)`, then angle between the tangents from `(alpha, beta)` to the circle `x^(2)+y^(2)=a^(2)`, is

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 the chord of contact of the tangents from the point (alpha, beta) to the circle x^(2)+y^(2)=r_(1)^(2) is a tangent to the circle (x-a)^(2)+(y-b)^(2)=r_(2)^(2) , then

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .

If two perpendicular tangents can be drawn from the point (alpha,beta) to the hyperbola x^(2)-y^(2)=a^(2) then (alpha,beta) lies on

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

The angle between the lines (x^(2)+y^(2))sin^(2)alpha=(x cos beta-y sin beta)^(2) is

If alpha and beta are connected by the relations alpha^(2)+alpha=1 and beta^(2)+beta=1, then the value of alpha^(2)+beta^(2) is eqal to

if s=cos^(2)alpha+cos^(2)beta then the value of cos(alpha+beta)*cos(alpha-beta) in terms of s is

If two perpendicular tangents are drawn from a point (alpha,beta) to the hyperbola x^(2) - y^(2) = 16 , then the locus of (alpha, beta) is