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

The equation (x^2)/(12-lambda)+(y^2)/(8-lambda)=1 represents

The equation (x^(2))/(10-lambda)+(y^(2))/(6-lambda)=1 represents

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

If the equation (x^(2))/( 3 - lambda) + (y^(2))/(lambda - 8) + 1 = 0 represents an ellipse, then (i) lambda lt 8 (ii) lambda gt 3 (iii) 3 lt lambda lt 8 (iv) lambda lt 3" or "lambda gt 8

Consider the equation (x^2)/(a^2+lambda)+(y^2)/(b^2+lambda)=1, where a and b are specified constants and lambda is an arbitrary parameter. Find a differential equation satisfied by it.

If the equation x^(2)+y^(2)+6x-2y+(lambda^(2)+3lambda+12)=0 represent a circle. Then

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

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 pair of lines through the origin for lambda=-3 an ellipse through A ,B ,C ,a n dD for lambda=-3 a parabola through A , B , C ,a n dD for lambda=-3 a circle for any lambda in R

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .