If `alpha` and `beta` are two points on the hyperbola `x^2/a^2-y^2/b^2=1` and the chord joining these two points passes through the focus `(ae,0)` then `ecos((alpha-beta)/2)`

If alpha and beta are two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and the chord joining these two points passes through the focus (ae,0) then e cos((alpha-beta)/(2))

If P(a sec alpha,b tan alpha) and Q(a secbeta, b tan beta) are two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that alpha-beta=2theta (a constant), then PQ touches the hyperbola

If (a sec alpha,b tan alpha) and (a sec beta ,b tan beta) be the ends of a chord of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passing through the focus (ae,0) then tan (alpha/2) tan (beta/2) is equal to

Tangent are drawn from every point on the line x+5y=4 to the ellipse (x^(2))/(5)+(y^(2))/(3)=1 ,then the corresponding chord of contact always passes through the point (alpha,beta) then (alpha+beta) equals

Tangent are drawn from every point on the line x+5y=4 to the ellipse (x^(2))/(5)+(y^(2))/(3)=1 ,then the corresponding chord of contact always passes through the point (alpha,beta) ,then (alpha+beta) equals

If alpha+beta=3 pi, then the chord joining the points alpha and beta for the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through which of the following points? Focus (b) Center One of the endpoints of the transverse exis.One of the endpoints of the conjugate exis.

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

Locus of the middle point of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 Which passes through a fixed point (alpha,beta) is hyperbola whose centre is (A) (alpha,beta) (B) (2 alpha,2 beta) (C) ((alpha)/(2),(beta)/(2)) (D) none

Let A(sec theta , 2 tan theta) and B(sec phi , 2 tan phi) , where theta+phi=pi//2 be two points on the hyperbola 2x^(2)-y^(2)=2 . If (alpha, beta) is the point of the intersection of the normals to the hyperbola at A and B, then (2beta)^(2) is equal to _________.