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 y=x+lambda is a tangent to an ellipse 2x^(2)+3y^(2)=1 then

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)

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

The eccentricity of the ellipse 9x^2+25y^2=225 is e then the value of 5e is

If tangents are drawn to the ellipse 2x^(2) + 3y^(2) =6 , then the locus of the mid-point of the intercept made by the tangents between the co-ordinate axes is

Let x+2=0 is a tangent to an ellipse whose foci are (1,3) and (4,7) .If e is the eccentricity of the ellipse then e^(2)+(266)/(97) is equal to

If P is a variable point on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose focii are S' and S and e_(1) is the eccentricity and the locus of the inceose centre of Delta PSS is an ellipse whose eccentricity is e_(2), then the value of (1+(1)/(e_(1)))e_(2)