If the equation `(5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2` represents an ellipse, then find values of `lambdadot`

If the equation 5[(x-2)^(2)+(y-3)^(2)]=(lambda^(2)-2 lambda+1)(2x+y-1)^(2) represents an ellipse then

if the equation (10x-5)^(2)+(10y-4)^(2)=lambda^(2)(3x+4y-1)^(2) represents a hyperbola then

The equation (x^(2))/(2-lambda)+(y^(2))/(lambda-5)+1=0 represents an elipse,if

Show that the equation (10x-5)^(2)+(10y-5)^(2)=(3x+4y-1)^(2) represents an ellipse, find the eccentricity of the ellipse.

Equation (2 + lambda)x^2-2 lambdaxy+(lambda -1)y^2-4x-2=0 represents a hyperbola if

If the equation x^(2)+y^(2)+2 lambda x+4=0 and x^(2)+y^(2)-4 lambda y+8=0 represent real circles then the valueof lambda can be

If the equation 3x^(2)+3y^(2)+6 lambda x+2 lambda=0 represents a circle,then the value of lambda. lies in