If a variable line y=kx+2h is tangent to an ellipse `2x^(2)+3y^(2)=6` , then locus of P(h,k) is a conic C whose eccentricity =`sqrt((a)/(b))` (where a and b are coprime natural number).Then the value of `(a)/(b)`

If the variable line y=kx+2h is tangent to an ellipse 2x^(2)+3y^(2)=6 then locus of P(h,k) is a conic C whose eccentricity is e then the value of 3e^(2) is

If the variable line y=kx+2h is tangent to an ellipse 2x^(2)+3y^(2)=6, then the locus of P(h,k) is a conic C whose eccentricity is 3 . Then the value of 3e^(2) is

The line 3x+5y-15sqrt(2) is a tangent to the ellipse (x^(2))/(25)+(y^(2))/(9)=1 at a point whose eccentric angle is

If area of rectangle formed by the perpendiculars drawn from centre of ellipse (x^(2))/(9)+(y^(2))/(16)=1 to the tangent and normal at the point (P((3)/(sqrt(2)),2sqrt(2))) on ellipse is ((a)/(b)) (where a and b are coprime numbers) then (a-3b) equals

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

The locus of point of intersection of tangents to an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at two points the sum of whose eccentric angles is constant is