Suppose (h,k) lies on the circle `x^(2)+y^(2)=4`, and (2h+1,3k+2) lies on an ellipse with eccentricity e, then `9e^(2)` equals

Suppose (h, k) lies on the circle x^2 + y^2 =4, then (2h + 1, 3k + 2) lies on an ellipse with eccentricity e, then e^2 equals

3x^2+4y^2-6x+8y+k=0 represents an ellipse with eccentricity 1/2,

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 e_(1) is the eccentricity of the conic 9x^(2)+4y^(2)=36 and e_(2) is the eccentricity of the conic 9x^(2)-4y^(2)=36 then e12-e22=2 b.e22-e12=2c.2 3

Let E be an ellipse such that x+y= 2sqrt5 is a tangent to E and E passes through (3,-1). If axes of E are along the coordinates axes and e is the eccentricity of E, then e^2 equals _____

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)

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

If e be the eccentricity of ellipse 3x2+2xy+3y^(2)=1 then 8e^(2) is