If the chord joining points `P(alpha)a n dQ(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(a/2)tan(beta/2)=-(b^2)/(a^2)dot`

If a chord P_(theta) Q_(phi) of an ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 subtands a right angle at the vertex A (a,0), then tan ((theta)/(2))* tan ((phi)/(2))=

If a chord PQ , joining P (theta) " Q and " (phi) , of an ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 , subtands a right angle at its centre , then tan theta * tan phi =

If tan theta_(1)*tan theta_(2)=(a^(2))/(b^(2)) then the chord Joining two points theta_(1) and theta_(2) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 will subtend a right angle at (A) focus (B) centre (C) end of the major axis (D) end of the major axis

If the chord,joining two points whose eccentric angles are alpha and beta, cuts the major axis ofthe ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at a distance crromn the centre,then tan alpha/2.tan beta/2 is equal to

P is any point lying on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(agtb) whose foci are S and S' . If anglePSS'=a and anglePS'S=beta , then the value of tan.(alpha)/(2)tan.(beta)/(2) is

if 2tan beta+cot beta=tan alpha then prove that cot beta=2tan(alpha-beta)

If a chord joining two points whose eccentric angles are alpha and beta so that tan alpha.tan beta=-(a^(2))/(b^(2)), subtend an angle theta at the centre of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then theta=

if c o* x=cos alpha.cos beta then prove that tan((x+alpha)/(2))*tan((x-alpha)/(2))=(tan^(2)beta)/(2)

If (alpha-beta)=(pi)/(2) ,then the chord joining the points whose eccentric angles are alpha and beta of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(k) , then ( 5k^(2)+2) is equal to