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

If x+y sqrt(2)=2sqrt(2) is a tangent to the ellipse x^(2)+2y^(2)=4 ,then the eccentric angle of the point of contact is

Show that the line y= x + sqrt(5/6 touches the ellipse 2x^2 + 3y^2 = 1 . Find the coordinates of the point of contact.

Does the straight line (x)/(a)+(y)/(b)=2 touch the ellipse ((x)/(a))^(2)+((y)/(b))^(2)=2? If it touches, find the coordinates of the point of contact.

Find the locus of the point of intersection of the tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) if the difference of the eccentric angles of their points of contact is 2 alpha.