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

P and Q are points on the ellipse x^2/a^2+y^2/b^2 =1 whose center is C . The eccentric angles of P and Q differ by a right angle. If /_PCQ minimum, the eccentric angle of P can be (A) pi/6 (B) pi/4 (C) pi/3 (D) pi/12

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

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

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

Let S and S'' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS'' The eccentricity of the locus oc the P is (a) ellipse (b) hyperbola (a) parabola (d) circle

In the ellipse (x^(2))/(6)+(y^(2))/(8)=1 , the value of eccentricity 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) .

If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

The eccentricity of the ellipse (x^(2))/(36)+(y^(2))/(25)=1 is