If the variable line `y=k x+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___________

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

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)

If the line y=3x+k is tangent to the parabola y^2=4x then the value of K is

The line 3x-4y=12 is a tangent to the ellipse with foci (-2,3) and (-1,0). Find the eccentricity of the ellipse.

The line 3x+5y=k touches the ellipse 16x^(2)+25y^(2)=400 ,if k 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