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 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 (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

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 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

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.

Show that the line x + y + 1=0 touches the hyperbola x^(2)/16 -y^(2)/15 = 1 and find the co-ordinates of the point of contact.

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) .

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 the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is