If `x/a+y/b=sqrt(2)` touches the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` , then find the eccentric angle `theta` of point of contact.

If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1 , then fin the ecentric angle theta of point of contact

If (sqrt(3))b x+a y=2a b touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then the eccentric angle of the point of contact is (a) pi/6 (b) pi/4 (c) pi/3 (d) pi/2

Find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.

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))

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) .

The line y = 2x + c touches the ellipse (x^2)/(16) + (y^2)/(4) = 1 if c is equal to

Show that the line x-y + 4 =0 is a tangents to the ellipse x^(2) + 3y^(2) =12 . Also find the coordinates of the points of contact.

If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci Sa n dS ' and eccentricity e , then prove that the area of S P S ' is basqrt(a^2-alpha^2)