Find the vertex the focus and the directrix Draw the graph o

Find the vertex, the focus, and the directrix. Draw the graph of y-5y-9-0 2 The focus is 3 Type an ordered pair.) What is the directrix? Select the correct choice below and fill in the answer box to complete your choice. 23 0 A. The directrix is y B. The directrix is x 2 Use the graphing tool to graph the equation

Solution

y²-5y -x+9=0

y²-5y=x-9

y²-5y +25/4 =x-9+25/4

(y -5/2)² = x-11/4

x=(y - 5/2)²+ 11/4

So the vertex is (5/2 , 11/4)

Focus =(h +(1/4a),k) = (5/2 +1/4 ,11/4) = (11/4,11/4)