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 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)=

P( asec alpha, b tan alpha ) and Q (a sec beta, b tan beta) are two given points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1. Show that the equation of the chord PQ is (x)/(a) cos (alpha - beta)/(2) - (y)/(b) sin (alpha + beta)/(2) = cos (alpha+beta)/(2).

Straight line joining the points (2,3) and (-1,4) passes through the point (alpha, beta) if

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 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

If alpha+beta=3pi , 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.