Find the value of `lamda` if the equation `(x-1)^(2)+(y-2)^(2)=lamda(x+y+3)^(2)` represents a parabola. Also, find its focus, vertex, the equation of its directrix, the equation of axis, the equation of axis, the equation of 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.

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.

Find the equations of normal to the parabola y^2=4a x at the ends of the latus rectum.

Find the equation of the ellispe whose latus rectum is 5 and e = 2/3

For the parabola y^2 = 8x , write its focus and the equation of the directrix.

Find the equation of the hyperbola where foci are (0,+-12) and the length of the latus rectum is 36 .

Find the equation of a parabola having its focus at S(2,0) and one extremity of its latus rectum at (2, 2)

Find the equation of an ellipse whose eccentricity is 2/3, the latus rectum is 5 and the centre is at the origin.

The length of the latus rectum of 3x^(2) -4y +6x - 3 = 0 is

The equation of the latus rectum of a parabola is x+y=8 and the equation of the tangent at the vertex is x+y=12. Then find the length of the latus rectum.