If a focal chord of an ellipse `y^(2)=b^(2)(1-x^(2))` cuts the ellipse at the points whose eccentric angles are `(5 pi)/(12)` and `(23 pi)/(12)` ,then the value of `b(b<1)` is

Find the equation of normal to the ellipse (x^(2))/(16)+(y^(2))/(9) = 1 at the point whose eccentric angle theta=(pi)/(6)

The equation of normal to the ellipse x^(2)+4y^(2)=9 at the point wherr ithe eccentric angle is pi//4 is

If omega is one of the angles between the normals to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 (b>a) at the point whose eccentric angles are theta and pi/2+theta , then prove that (2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))

If omega is one of the angles between the normals to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the point whose eccentric angles are theta and pi/2+theta , then prove that (2cotomega)/(sin2theta)=(e^2)/(sqrt(1-e^2))

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

If PSQ is a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 agtb then harmonic mean of SP and SQ is

Let P and Q be two points on the ellipse x^(2) + 4y^(2) = 16 , whose eccentric angles are (pi)/(4) and (3x)/(4) respectively. Then the area of the triangle OPQ is

The area of the parallelogram formed by the tangents at the points whose eccentric angles are theta, theta +(pi)/(2), theta +pi, theta +(3pi)/(2) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 at points whose eccentric angles differ by pi/2, then find the value of (a^2l^2+b^2m^2)/(n^2) .