If `(alpha+beta)`and `(alpha-beta)`are the eccentric angles of the points P and Q respectively on the ellipse `x^2/25+y^2/9=1`.Show that the equation of the chord PQ is `x/5cosalpha+y/3sinalpha=cosbeta`

If (alpha +beta ) and (alpha - beta ) are the eccentric angles of the points P and Q respectively on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 show that the equation of the chord PQ is (x)/(a) cos alpha+(y)/(b)sin alpha = cos beta .

If the eccentric angles of the any two points P,Q on the ellipse x^2/a^2+y^2/b^2=1 are (alpha+beta) and (alpha-beta) resp.Show that the equation of chord PQ is x/a cosalpha+y/b sinalpha=cosbeta

If alpha and beta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))

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).

The eccentric angles of the two points P and Q on the ellipse x^2/a^2+y^2/b^2=1(a>b) are theta and phi resp.If the chord PQ makes angle 90^@ with the vertex (a,0)of the ellipse then show that tan(theta/2)tan(phi/2)=-b^2/a^2

If cosalpha+cosbeta=2/3 and sinalpha+sinbeta=2/5 then find the vvalue of tan((alpha+beta)/2)

Tangents PQ and PR are drawn from the point (alpha, beta) to the circle x^(2)+y^(2)=a^(2) . Show that the area of Delta PQR is (a(alpha^(2)+ beta^(2)-a^(2))^(3//2))/(alpha^(2)+ beta^(2)) .

Find the point (alpha,beta) on the ellipse 4x^2+3y^2=12 , in the first quadrant, so that the area enclosed by the lines y=x ,y=beta,x=alpha , and the x-axis is maximum.

If alpha and beta be the eccentric angles of the extremities of a focal chord of the hyperbola b^(2)x^(2) - a^(2)y^(2) = a^(2)b^(2) , show that, tan(alpha)/(2)tan(beta)/(2) = -(e-1)/(e+1) , (e-1)/(e+1) (e is the eccentricity of the hyperbola.).