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 equation of its directrix , equation of its axis , coordinates of the vertex equation of its latus rectum and extremities of the latus rectum

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.

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.

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, rectum.

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 coordinates of its vertex, the equation of its latus rectum

y^2+2y-x+5=0 represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.

y^2+2y-x+5=0 represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.

y^2+2y-x+5=0 represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.

y^(2)+2y-x+5=0 represents a parabola. Find its vertex,equation of axis,equation of latus rectum,coordinates of the focus, equation of the directrix,extremities of the latus rectum,and the length of the latus rectum.

If the point (2, 3) is the focus and x = 2y + 6 is the directrix of a parabola, find (i) The equation of the axis. (ii) The co-ordinates of the vertex. (iii) Length of the latus rectum. (iv) Equation of the latus rectum.