Question

Find the Vertex, Focus directrix and Length of the latus rectum of the parabola (i) x²- 4x - 5y - 1 = 0​

Answer 1

Answer:

Step-by-step explanation:

The given equation is written as (x - 2)2 = 5(y + 1) = 4(5/4)(y + 1) Let X = x − 2 and Y = y + 1 so that  X2 = 4aY where a = 5/4. Therefore 1.  The vertex (X = 0, Y = 0) is (2, -1) 2.  The focus (X = 0,Y = a) is (x = 2, y + 1 = 5/4) = (2, 1/4) 3.  The directrix equation is Y = -a or y + 1 = -5/4 or 4y + 9 = 0 4.  The latus rectum is 4a = 4(5/4) = 5.Read more on Sarthaks.com - https://www.sarthaks.com/519736/find-the-vertex-focus-directrix-and-latus-rectum-of-the-parabola-x-2-4x-5y-1-0