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`

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

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

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

If eccentric angle of a point lying in the first quadrant on the ellipse x^2/a^2 + y^2/b^2 = 1 be theta and the line joining the centre to that point makes an angle phi with the x-axis, then theta - phi will be maximum when theta is equal to

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 subtends a right angle at the vertex A(a ,0), then prove that tan(alpha/2)tan(beta/2)=-(b^2)/(a^2)dot

If the eccentric angles of the two points on the ellipse (x^(2))/(a^(2)) =(y^(2))/(b^(2)) = 1 (a^(2)gt b^(2)) and theta_(1) and theta_(2) then prove that the equation of chord passing through these two point is (x)/(a)"cos"(theta_(1)+theta_(2))/(2)+(y)/(b)"sin"(theta_(1)+theta_(2))/(2)="cos" (theta_(1)-theta_(2))/(2) .

Find the locus of middle points of chords of the ellipse x^2/a^2+y^2/b^2=1 which subtend right angles at its centre.

If x costheta+ysintheta=xcosphi+ysinphi then show that y=x tan ((theta+phi)/2)

The slop of the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 at the point (a cos theta, b sin theta) - is