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`

Does equation (5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2) represents a parabola ?

Find the value of lambda if the equation (x-1)^2+(y-2)^2=lambda(x+y+3)^2 represents a parabola. Also, find its focus, the equation of its directrix, the equation of its axis, the coordinates of its vertex, the equation of its latus rectum, the length of the latus rectum, and the extremities of the latus rectum.

If the equations 2x-lambday+5z=7 and lambda x-8y-10z+14=0 represent the same plane then lambda is :

The equation (x^(2))/(9-lambda)+(y^(2))/(4-lambda) =1 represents a hyperbola when a lt lambda lt b then (b-a)=

Suppose the circle having equation x^2+y^2=3 intersects the rectangular hyperbola x y=1 at points A ,B ,C ,a n dDdot The equation x^2+y^2-3+lambda(x y-1)=0,lambda in R , represents. (a)a pair of lines through the origin for lambda=-3 (b)an ellipse through A ,B ,C ,a n dD for lambda=-3 (c)a parabola through A , B , C ,a n dD for lambda=-3 (d)a circle for any lambda in R

If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0 , represents a pair of straight lines, then the value of lambda is

Which of the following is/are true? There are infinite positive integral values of a for which (13 x-1)^2+(13 y-2)^2=((5x+12 y-1)^2)/a represents an ellipse. The minimum distance of a point (1, 2) from the ellipse 4x^2+9y^2+8x-36 y+4=0 is 1 If from a point P(0,alpha) two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 then |alpha|<9/4dot If the length of the latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1sqrt(3)

If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negative roots, then the least value of lambda equals__________.

If f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)(lambda^2-5lambda+3)x+10 is a decreasing function for all x in R , find the permissible values of lambdadot

If lambda_(1) and lambda_(2) be two values of lambda for which the expression x^(2)+(2-lambda) x+lambda-(3)/(4) becomes a perfect square, then calculate the value of (lambda_(1)^(2)+lambda_(2)^(2)) .