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)` .

If the line lx+my +n=0 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then

If the line Ix + my +n=0 cuts the ellpse (x^(2))/(a^(2))+(Y^(2))/(b^(2))=1 in point eccentric angles differ by pi//2 , then

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

Find the condition so that the line px+qy=r intersects the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 in points whose eccentric angles differ by (pi)/(4) .

The points on the ellipse (x^(2))/(25)+(y^(2))/(9)=1 Whose eccentric angles differ by a right angle are

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 area of the triangle formed by three points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentric angles are alpha,beta and gamma is

If the line x+2y+4=0 cutting the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 in points whose eccentric angies are 30^(@) and 60^(@) subtends right angle at the origin then its equation is

Find the sum of squares of two distances of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose extremities have eccentric angles differ by (pi)/(2) and sow that is a constant.