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 +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 (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

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

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).

If alpha and beta be the roots of the equation x^2+3x+4=0 find the equation whose roots are (alpha+beta)^2 and (alpha-beta)^2 .

IF the roots of the equation 3x^2+8x+2=0 are alpha,beta then (1/alpha+1/beta) =

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

If alpha+beta=(pi)/(2) , then prove that cosalpha=sqrt((sinalpha)/(cosbeta)-sinalphacosbeta)

If the roots of the equation ax^2-bx+a=0 be alpha and beta , show that the equation with roots alpha^2+1 and beta^2+1 will be a^2x^2-b^2x+b^2=0

If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci S a n d S ' and eccentricity e , then prove that the area of Δ S P S ' is be sqrt(a^2-alpha^2)